Sequential Decreasing-Width Number Triangle in PHP

Beginner

⏱️ 8 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Nested Loops + Format

Sequential decreasing width number triangle pattern output in PHP

Overview

What You’ll Learn

The sequential decreasing-width number triangle prints consecutive integers in rows that get shorter each line. This tutorial covers the shape rule, the $k counter, nested loops, printf alignment, a live preview, algorithm steps, worked PHP examples, edge cases, and complexity.

Shape Rule

Shrinking row width

Row 1 prints $rows numbers, row 2 prints $rows-1, down to one number on the last line.

k Counter

Global sequence

$k = 1 tracks the next value; $k++ after each print keeps the sequence continuous.

Outer Loop

Rows

for ($i = 1; $i <= $rows; $i++) walks from the widest row to the narrowest.

Inner Loop

Decreasing count

for ($j = $rows; $j >= $i; $j--) runs fewer times as $i grows.

Live Preview

1–20 rows

Pick a row count and draw the sequential triangle instantly in the browser.

O(n²)

Complexity

Total values = n(n+1)/2; extra memory stays O(1).

Introduction

A sequential decreasing-width number triangle prints consecutive integers while each row gets one value shorter. With $rows = 5, the output is 1 2 3 4 5, then 6 7 8 9, then 10 11 12, 13 14, and 15.

In PHP you solve it with two nested for loops and a shared $k counter: the outer loop picks the row, the inner loop prints $rows - $i + 1 formatted numbers with printf("%3d", $k++), then echo PHP_EOL moves to the next line.

Why it matters?

It teaches counter-driven output and formatted columns — key skills before harder number-pattern variants.

Key Highlights

Shrinking Row Width

Row $i prints $rows - $i + 1 consecutive values.

k Counter

printf("%3d", $k++) keeps columns aligned.

Format Then Break

printf("%3d", $k++) in the inner loop; echo PHP_EOL after.

Series Foundation

Follow Program 37 palindrome rows; continue to Program 39 rotating numbers.

In short: for each row $i from 1 to $rows, print $rows - $i + 1 consecutive numbers with printf("%3d", $k++), then call echo PHP_EOL.

Foundation

📝 Problem & Approach

Given a positive integer $rows, print consecutive integers starting at 1 in a triangle where row $i contains exactly $rows - $i + 1 values.

PHP

// First 5 rows (conceptual shape)
//   1  2  3  4  5
//   6  7  8  9
//  10 11 12
//  13 14
//  15

Inputs & Outputs

Item	Type	Description
`$rows`	int	Number of triangle lines to print (typically ≥ 1).
Printed output	text	Left-aligned rows of consecutive integers; row `$i` has `$rows - $i + 1` values.

Minimal workflow

Pseudocode

for i from rows down to 1:
    if i is even:
        for j from i down to 1: print j
    else:
        for j from 1 to i: print j
    print newline

Approach comparison

Approach	Idea	Best for
Nested loops + k counter	Outer rows + inner shrinking width + format	Learning and interviews
Custom start k	Change initial k instead of 1	Variations and demos

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Walk each row	`for ($i = 1; $i <= $rows; $i++)`
Print shrinking count	`for ($j = $rows; $j >= $i; $j--) printf("%3d", $k++);`
End the row	`echo PHP_EOL;`
Wider columns	`printf("%4d", $k++);` for larger totals
Program 37 variant	Palindrome per row instead of global sequence

Compare

📋 echo vs printf vs sprintf

Same triangle — different ways to emit aligned numbers.

echo

no padding

Digits run together — columns misalign at 10+

printf

%3d

Right-aligns each value in a 3-character field

sprintf

returns string

Builds formatted text without printing directly

Learning tip

$k counter

Master the $k++ pattern before wider field widths

Context

When This Pattern Shows Up

Reach for this pattern when teaching counters and formatted output inside nested loops.

First lab exercise
Most PHP pattern series start here before pyramids and diamonds.
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with fgets(STDIN) for a flexible row count.
Gateway to variants
Compare Program 37 palindrome rows and Program 39 rotating numbers next.
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.

Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.

Interactive

🔮 Live Preview

Choose a row count between 1 and 20 and draw the sequential decreasing-width triangle in the browser.

Hands-On

Examples Gallery

Three complete PHP programs — fixed row count, fgets(STDIN) input, and a custom starting value for $k. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows with nested loops, a $k counter, and formatted output.

Example 1 — Fixed `$rows = 5`

Hard-coded height — ideal for first demos and screenshots.

PHP

<?php
$rows = 5;
$k = 1;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $rows; $j >= $i; $j--) {
        printf("%3d", $k++);
    }
    echo PHP_EOL;
}

How It Works

When $i = 1, the inner loop runs 5 times and prints 1 through 5. When $i = 2, it prints 6 through 9, and so on until the last row prints 15. echo PHP_EOL after the inner loop starts the next row.

📈 Practical Variant

Let the user choose the height at runtime.

Example 2 — User Input Version

Read the row count with fgets(STDIN).(int) trim(fgets(STDIN)) (check is_numeric() in real apps).

PHP

<?php
echo "Enter the number of rows: ";
$input = trim(fgets(STDIN));
if (!is_numeric($input)) return;
$rows = (int) $input;
if ($rows < 1) return;

$k = 1;
for ($i = 1; $i <= $rows; $i++) {
    for ($j = $rows; $j >= $i; $j--) {
        printf("%3d", $k++);
    }
    echo PHP_EOL;
}

How It Works

Same nested-loop core as Example 1; only the source of $rows changes. Non-numeric input throws invalid input with (int) trim(fgets(STDIN)) — check is_numeric() for safer labs.

⚡ Variation

Same shape with a different starting value for the sequence.

Example 3 — Custom Start `$k = 10`

Initialize $k with any starting value — the inner loop logic stays the same.

PHP

<?php
$rows = 5;
$k = 10;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $rows; $j >= $i; $j--) {
        printf("%3d", $k++);
    }
    echo PHP_EOL;
}

How It Works

Only the initial value of $k changes. The shrinking inner loop still prints $rows - $i + 1 values per row. Great for variations once you understand the default $k = 1 version.

🧠 How the Algorithm Prints Rows

Set up

Set $rows = 5; and use fgets(STDIN) when reading input. Set loop variables $i, $j, $k.

Setup

Outer loop (rows)

for ($i = 1; $i <= $rows; $i++) selects the current row from widest to narrowest.

Row

Inner loop (values)

for ($j = $rows; $j >= $i; $j--) prints $rows - $i + 1 numbers with printf("%3d", $k++).

New line

echo PHP_EOL ends the row so the next outer iteration starts fresh.

Break

Triangle complete

Total digit prints: 1+2+…+n = n(n+1)/2 — O(n²) time, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `$rows = 4`

Trace each outer-loop value of $i, the inner-loop count, and the values printed via $k.

`$i`	Inner runs	`$k` range	Printed row
`1`	4	`1..4`	`1 2 3 4`
`2`	3	`5..7`	`5 6 7`
`3`	2	`8..9`	`8 9`
`4`	1	`10`	`10`

Total value prints: 1 + 2 + 3 + 4 = 10 = 4×5/2.

Use Cases

Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.

1. Teaching Nested Loops

Clearest visual proof that outer and inner bounds interact.

Example: change $j <= $i and watch the shape change.

2. Pattern Series Base

Foundation for inverted, pyramid, diamond, and hollow variants.

Example: change $k start to 100 for a shifted sequence.

3. Console Formatting Drills

Practice echo vs echo PHP_EOL without complex math.

Example: put echo PHP_EOL inside the inner loop by mistake.

4. Character Substitution

Swap digits for letters, stars, or spaced output once the loop works.

Example: use %4d when values exceed two digits.

5. Complexity Intuition

Triangular totals make O(n²) concrete for beginners.

Example: count printed digits for n = 10 still → 55.

6. Input Validation Labs

Pair the pattern with fgets(STDIN) and positive-row checks.

Example: reject rows <= 0 and re-prompt.

Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.

Advantages

Why this pattern earns a permanent spot in beginner PHP courses.

1. Instant Visual Feedback
Wrong bounds show up immediately as a broken staircase.
2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Invert, center, hollow, or change the fill character with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.

Pro Tip: learn the $k-counter nested-loop version first; then try custom start values or wider format widths.

Usage Tips

Small habits that keep number-pattern code clean.

1. Name Bounds Clearly
Use $rows (or n) and keep $i/$j for row/column — or rename to row/col.
2. Prefer trim(fgets(STDIN))
Avoid crashes when the user types letters instead of a number.
3. Keep echo PHP_EOL Outside
Only call echo PHP_EOL after the inner loop finishes the row.
4. Pick Field Width Early
Use %4d or wider when total values exceed 99.
5. Dry-Run One Small n
Trace $rows = 3 on paper before coding larger demos.

Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put echo PHP_EOL inside the inner loop.

Common Pitfalls

Mistakes that commonly break sequential decreasing-width number patterns.

1. echo PHP_EOL Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use printf("%3d", $k++) for values; echo PHP_EOL only after the inner loop.
2. Wrong Inner Bound
Using $j <= $rows on every row prints a rectangle; resetting $k each row breaks the sequence.
→ Keep for ($j = $rows; $j >= $i; $j--) and one shared $k.
3. Forgetting the Row Break
Omitting echo PHP_EOL glues every digit onto one endless line.
→ Always end the row after the inner loop.
4. Unchecked CLI input
Letters or empty input throw undefined rows.
→ Prefer trim(fgets(STDIN)) and re-prompt on failure.
5. Off-by-One on 0-Based Loops
Switching to $i = 0 without adjusting the inner bound prints an empty first row or wrong counts.
→ If 0-based, print $i with wrong inner bound (e.g. $j <= $i + 1).

Edge Cases

Check these inputs before calling the solution done.

$rows = 1

Single digit

Output is just 1 on one line.

$rows = 0

Empty pattern

Outer loop never runs — print nothing or show a message.

Negative

`rows < 0`

Treat as invalid; re-prompt instead of silent empty output.

Large n

Many rows

Output grows as n²/2 characters — fine for labs, noisy for huge n.

Bad input

Non-numeric CLI input

Unchecked fgets(STDIN) leaves $rows unset — call is_numeric($input) first.

Fill char

Custom start k

Initialize $k to any value — the sequence continues from there.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Palindrome number triangle

Build symmetric rows like 4321234
Continue with Program 37

2. Rotating number pattern

Shift the sequence each row (23451, 34521, …)
Continue with Program 39

3. Upside-down triangle

Start with one number and grow row width each line
Reverse outer and inner loop bounds

4. Wider format

Use %4d or %5d for larger triangles
Keeps columns aligned past two digits

Important

Notes

Triangular count. Total digit prints for n rows is n(n+1)/2 — hence O(n²) time.
print stays on the line; println advances — mix them carefully.
Validate $rows > 0 for interactive programs; $rows = 1 should print a single 1.
This page is left-aligned. Centered pyramids need leading spaces — covered later in the series.

Quick Takeaway: outer loop picks the row, inner loop prints shrinking count with $k++, then break the line.

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–2)	`O(rows²)`	`O(1)`
Custom start k (Example 3)	`O(rows²)`	`O(1)`

Wrap Up

🎉 Conclusion

The sequential decreasing-width number triangle combines nested loops with a shared $k counter and formatted output — a natural step after palindrome rows. Master the default $k = 1 version, then optionally change the start value or field width.

Practice the three examples above, then continue to Program 39 for the rotating number pattern.

Row $i prints $rows - $i + 1 consecutive values — keep printf("%3d", $k++) for digits and echo PHP_EOL for the break.

View Examples Gallery Continue to Program 39

Pro Tips

💡 Best Practices

✅ Do

Explain $k counter and shrinking inner bound before coding
Use printf("%3d", $k++) for values and echo PHP_EOL after each row
Validate rows ≥ 1 for interactive programs
Check is_numeric($input) return value before using $rows
State O(n²) time when asked about complexity

❌ Don’t

Call echo PHP_EOL inside the inner digit loop
Reset k inside the outer loop (breaks the global sequence)
Skip the newline after each row
Ignore bad console input in user-facing demos
Skip the $rows = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this sequential pattern

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

Row i prints rows-i+1 values

Definition

↻ 02

Outer loop

Controls each row

Code

k 03

$k counter

$k++ after each print

Logic

# 04

printf %3d

Aligns columns

I/O

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why does this pattern print 15 numbers for 5 rows?

Because the row lengths are 5, 4, 3, 2, and 1. Their sum is 5+4+3+2+1 = 15, which equals n(n+1)/2.

What does %3d do in printf?

%3d prints an integer right-aligned in a field width of 3 characters, which keeps columns aligned when numbers reach two digits.

Why use a k counter instead of printing j?

Each row prints a different count of numbers, but the sequence must continue globally (1, 2, 3, ...). $k stores the next value and increments after every print.

Can I start from a different number?

Yes. Initialize $k with your starting value instead of 1, for example $k = 10.

How is this different from Program 37?

Program 37 builds a palindrome on each row (4321234). Program 38 prints one continuous ascending sequence with shrinking row widths.

What is the time complexity?

O(n²) where n is the number of rows. Total printed values equal 1+2+…+n = n(n+1)/2.

How should I read the row count safely?

Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int.

What happens if rows is 0 or negative?

The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.

Did you Know? 🔊

Row $i prints $rows - $i + 1 consecutive numbers via a shared $k counter. Total values for n rows is the triangular number n(n+1)/2 — 15 when $rows = 5.

Continue to Program 39

Move on to the rotating number pattern in the PHP number-pattern series.

Program 39 tutorial →

About the author

Mari Selvan M P 🔗

Developer, cloud engineer, and technical writer

Experience 12 years building web and cloud systems
Focus Full Stack Development, AWS, and Developer Education

I write practical tutorials so students and working developers can learn by doing—from databases and APIs to deployment on AWS.

AWS Certified Developer – Associate (Credly)

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PHP Number Pattern 37 — Palindrome Number Triangle PHP Number Pattern 39 — Rotating Number Pattern

Sequential Decreasing-Width Number Triangle in PHP

What You’ll Learn

Shape Rule

k Counter

Outer Loop

Inner Loop

Live Preview

O(n²)

Introduction

Why it matters?

Shrinking Row Width

k Counter

Format Then Break

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 echo vs printf vs sprintf

When This Pattern Shows Up

First lab exercise

Nested-loop warm-up

Console I/O practice

Gateway to variants

Not a UI layout tool

🔮 Live Preview

Examples Gallery

📚 Getting Started

Example 1 — Fixed $rows = 5

How It Works

📈 Practical Variant

Example 2 — User Input Version

How It Works

⚡ Variation

Example 3 — Custom Start $k = 10

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop (rows)

Inner loop (values)

New line

Triangle complete

🔎 Worked Walkthrough — $rows = 4

Use Cases

1. Teaching Nested Loops

2. Pattern Series Base

3. Console Formatting Drills

4. Character Substitution

5. Complexity Intuition

6. Input Validation Labs

Advantages

1. Instant Visual Feedback

2. Minimal Concepts

3. Easy to Extend

4. O(1) Extra Memory

Usage Tips

1. Name Bounds Clearly

2. Prefer trim(fgets(STDIN))

3. Keep echo PHP_EOL Outside

4. Pick Field Width Early

5. Dry-Run One Small n

Common Pitfalls

1. echo PHP_EOL Inside the Inner Loop

2. Wrong Inner Bound

3. Forgetting the Row Break

4. Unchecked CLI input

5. Off-by-One on 0-Based Loops

Edge Cases

Single digit

Empty pattern

rows < 0

Many rows

Non-numeric CLI input

Custom start k

🎯 Practice Problems

1. Palindrome number triangle

2. Rotating number pattern

3. Upside-down triangle

4. Wider format

Example 1 — Fixed `$rows = 5`

Example 3 — Custom Start `$k = 10`

🔎 Worked Walkthrough — `$rows = 4`

2. Prefer `trim(fgets(STDIN))`

`rows < 0`