Palindrome Number Triangle in Python

Beginner

⏱️ 9 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Nested Loops + Symmetry

Palindrome number triangle output in Python (1, 212, 32123, 4321234, 543212345)

Overview

What You’ll Learn

The palindrome number triangle prints 1, then 212, then 32123, … — a natural follow-up after Program 36’s right-aligned decreasing triangle. This tutorial covers descending and ascending inner loops, row symmetry, nested loops, a live preview, worked Python examples, edge cases, and complexity.

Shape Rule

Palindrome row

Row i prints i down to 2, then 1 up to i — a symmetric sequence.

Outer Loop

i = 1..rows

for i in range(1, rows + 1): — one palindrome row per iteration.

Left Half

i..2

for j in range(i, 1, -1): — prints the descending left side of the palindrome.

Right Half

1..i

for j in range(1, i + 1): — completes the palindrome with ascending digits.

Live Preview

3–7 rows

Pick a row count and draw the palindrome number triangle in the browser.

O(n²)

Complexity

Digits per row = 2i - 1 — total digits = n².

Introduction

A palindrome number triangle prints a symmetric sequence on each row: 1, then 212, then 32123, and so on. With rows = 5, each row reads the same forward and backward.

In Python you use two inner loops per row: print j from i down to 2, then from 1 up to i, then print().

Why it matters?

It combines descending and ascending inner loops to build symmetry — a step after Program 36’s right-aligned decreasing pattern.

Key Highlights

i..2 desc

Left half.

1..i asc

Right half.

2i - 1

Digits per row.

Series Foundation

Follow Program 36; continue to Program 38 next.

In short: outer i = 1..rows, desc j = i..2, asc j = 1..i, then print().

Foundation

📝 Problem & Approach

Given rows = 5, print a palindrome number triangle: for each row i, print descending i..2 then ascending 1..i.

Python

# rows = 5
# 1
# 212
# 32123
# 4321234
# 543212345

Inputs & Outputs

Item	Type	Description
`rows`	int	Triangle height — number of palindrome lines to print.
`i`	int	Outer loop — current row (1 to rows).
`j`	int	Inner loop — descending (`i..2`) or ascending (`1..i`).

Minimal workflow

Pseudocode

for i from 1 to rows:
    for j from i down to 2: print j
    for j from 1 to i: print j
    print newline

Approach comparison

Approach	Idea	Best for
Fixed rows	`1`, `212`, …	Learning and interviews
User-input rows	`int(input(...))`	Configurable triangle size
Compact trace	`rows = 3` on paper first	Debugging loop bounds

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Outer loop	`for i in range(1, rows + 1):`
Left half (desc)	`for j in range(i, 1, -1): print(j, end="")`
Right half (asc)	`for j in range(1, i + 1): print(j, end="")`
End the row	`print()`
User input	`int(input())`

Compare

📋 Fixed vs User Input vs Compact Demo

Same palindrome triangle — different ways to control the row count.

Outer loop

i = 1..rows

One palindrome row per iteration

Left half

j = i..2

Descending digits

Right half

j = 1..i

Ascending digits

Learning tip

2i - 1

Digits per row

Context

When This Pattern Shows Up

Reach for this pattern when teaching symmetry, dual inner loops, and palindrome construction in nested loops.

After Program 36
Natural follow-up — replaces right alignment with symmetric palindrome rows built from two inner loops.
Symmetry drills
Practice descending then ascending loops to build mirrored sequences on each row.
Console I/O practice
Combine loops with input() and try/except ValueError for flexible row counts.
Gateway to variants
Compare Program 36 (decreasing) and Program 38 (next in series) 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 dual inner loops, formatted output, and O(n²) thinking.

Interactive

🔮 Live Preview

Choose a row count between 3 and 7 and draw the palindrome number triangle in the browser.

Hands-On

Examples Gallery

Three complete Python programs — fixed rows, user input, and a smaller trace demo. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows of the palindrome number triangle with descending and ascending inner loops.

Example 1 — Fixed `rows = 5`

Hard-coded row count — ideal for first demos and screenshots.

Python

rows = 5

for i in range(1, rows + 1):
    for j in range(i, 1, -1):
        print(j, end="")
    for j in range(1, i + 1):
        print(j, end="")
    print()

How It Works

When i = 3, the first loop prints 3 2, the second prints 1 2 3 — output 32123. When i = 1, only the ascending loop runs — output 1.

📈 User Input

Read the row count with input() and int() instead of hard-coding 5.

Example 2 — User input rows

Read rows with input() and int() (wrap in try/except ValueError in real apps).

Python

rows = int(input("Enter rows: "))
if rows < 1:
    raise SystemExit

for i in range(1, rows + 1):
    for j in range(i, 1, -1):
        print(j, end="")
    for j in range(1, i + 1):
        print(j, end="")
    print()

How It Works

Same palindrome core as Example 1; only rows comes from user input instead of being hard-coded as 5. Non-numeric input raises ValueError with bare int(input()) — use try/except for safer labs.

⚡ Smaller Demo

Run with rows = 3 to trace every row on paper before scaling up.

Example 3 — Compact `rows = 3`

Same descending and ascending loops with a smaller row count for quick tracing.

Python

rows = 3

for i in range(1, rows + 1):
    for j in range(i, 1, -1):
        print(j, end="")
    for j in range(1, i + 1):
        print(j, end="")
    print()

How It Works

Only rows changes from 5 to 3 — the two inner loops stay identical. Trace i = 1, 2, 3 on paper to see how each row grows symmetrically.

🧠 How the Algorithm Prints Rows

Set up

No imports needed for fixed rows; use input() when reading. Set loop variables i, j with rows = 5.

Setup

Outer loop walks rows

for i in range(1, rows + 1): — ascending outer loop; one palindrome row per iteration.

Row

Left half (descending)

for j in range(i, 1, -1): — prints i, i-1, ..., 2.

Mirror left

Right half (ascending)

for j in range(1, i + 1): — completes the palindrome: 1, 2, ..., i.

Mirror right

New line

print() ends the row after both inner loops finish.

Break

Palindrome triangle complete

Digits per row = 2i - 1 — total digits = n²; O(n²) time.

Trace

🔎 Worked Walkthrough — `rows = 5`

Trace each outer-loop value of i, left and right halves, and full row output.

`i`	Left half (`i..2`)	Right half (`1..i`)	Row output
`1`	—	`1`	`1`
`2`	`2`	`1, 2`	`212`
`3`	`3, 2`	`1, 2, 3`	`32123`
`4`	`4, 3, 2`	`1, 2, 3, 4`	`4321234`
`5`	`5, 4, 3, 2`	`1, 2, 3, 4, 5`	`543212345`

Digits per row = 2i - 1 — total digits = 1 + 3 + 5 + ... + (2n-1) = n².

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: swap the ascending and descending loops and watch the palindrome break.

2. Pattern Series Base

Foundation for symmetry-based patterns and mirrored sequences.

Example: compare with Program 36 (decreasing) and Program 38 next.

3. Console Formatting Drills

Practice concatenated digit output without spaces between numbers.

Example: add j + " " between digits for a spaced palindrome variant.

4. Padding character

Add leading spaces for center alignment once the two-loop structure works.

Example: print rows - i spaces before the descending loop.

5. Complexity Intuition

Triangular totals make O(n²) concrete for beginners.

Example: count digits for rows = 5 — total is 1+3+5+7+9 = 25 = 5².

6. Input Validation Labs

Pair the pattern with try/except ValueError and positive-row validation.

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 Python 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: trace i and both inner loops on paper for rows = 3 before coding — watch how each row grows symmetrically.

Usage Tips

Small habits that keep number-pattern code clean.

1. Two Inner Loops Per Row
Descending loop (j > 1) must run before ascending loop (j <= i).
2. Call try/except ValueError
Avoid undefined behavior when the user types letters instead of a number.
3. Keep newline outside inner loops
Only call print() after both inner loops finish the row.
4. Trace halves on Paper
Write left half (i..2) and right half (1..i) for each row before coding.
5. Dry-Run rows = 3
Trace i = 1..3 on paper before coding the full rows = 5 demo.

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

Common Pitfalls

Mistakes that commonly break palindrome number triangles.

1. Newline Inside an Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use print(j, end=""); print() only after both inner loops.
2. Wrong Loop Order
Running ascending before descending breaks the palindrome symmetry.
→ Always print descending j = i..2 first, then ascending j = 1..i.
3. Wrong Descending Bound
Using j >= 1 in the first loop duplicates the center digit.
→ Keep for j in range(i, 1, -1): — stop at 2, let the ascending loop print 1.
4. Including 1 Twice
Starting the descending loop at j >= 1 prints 1 twice in the middle.
→ Descending stops at j > 1; ascending starts at j = 1.
5. Bare int(input())
Letters or empty input raise ValueError with bare int(input()).
→ Catch ValueError and re-prompt on failure.

Edge Cases

Check these inputs before calling the solution done.

rows = 1

Single row

Output is just 1 — only the ascending loop runs.

rows = 0

Empty pattern

Outer loop never runs when rows < 1 — print nothing or show a message.

Negative

`rows < 1`

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

rows = 2

Smallest triangle

Two rows: 1 and 212.

Bad input

Non-numeric input

Bare int(input()) raises ValueError on bad input — use try/except first.

Large rows

Large row count

Total digits = rows² — grows quadratically with rows.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Right-aligned decreasing

Review Program 36
Right-aligned triangle with decreasing sequences

2. Next in series

Continue with Program 38
Next pattern in the number-pattern series

3. Palindrome trace

Prove on paper: row i has 2i - 1 digits
Left half = i..2, right half = 1..i

4. Safe input loop

Validate rows >= 1 after reading input
Then draw the triangle

Important

Notes

Palindrome rule. Outer i = 1..rows. Descending j = i..2, then ascending j = 1..i — row i prints 2i - 1 digits.
print(j, end="") stays on the line; print() advances — mix them carefully.
Validate rows >= 1 for interactive programs; rows = 1 prints a single 1.
Center digit is always 1 — compare with Program 36 where each row restarts from rows.

Quick Takeaway: outer i = 1..rows, desc j = i..2, asc j = 1..i, then print().

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–3)	`O(n²)`	`O(1)`
Smaller demo (Example 3)	`O(n²)`	`O(1)`

Wrap Up

🎉 Conclusion

The palindrome number triangle is a compact lesson in symmetry: print descending i..2, then ascending 1..i, and end each row with print(). Master the fixed-rows version, then try user input and a smaller trace demo.

Practice the three examples above, then continue to Program 38 for the next pattern in the series.

Descending loop must stop at j > 1 — validate rows when reading from the console.

View Examples Gallery Continue to Program 38

Pro Tips

💡 Best Practices

✅ Do

Use for i in range(1, rows + 1): in the outer loop
Left: for j in range(i, 1, -1): print(j, end="")
Right: for j in range(1, i + 1): print(j, end="")
Wrap int(input()) in try/except ValueError
State O(n²) time when asked about complexity

❌ Don’t

Call print() inside an inner loop
Run ascending loop before descending loop
Use j >= 1 in the descending loop (duplicates 1)
Ignore bad input() input in user-facing demos
Skip the rows = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this palindrome triangle

Print the pattern the beginner-friendly way.

Core concepts

△ 01

i..2 desc

Left half

Definition

↻ 02

1..i asc

Right half

Code

0 03

2i - 1

Digits/row

Code

↓ 04

Row break

print() after both inner loops

Shape

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why is this called a palindrome number pattern?

Each row reads the same forward and backward. For example, 4321234 is symmetric around the center digit 1.

How do the loops form the palindrome?

First, a loop prints i down to 2 (left half). Then another loop prints 1 up to i (right half). Together they create a mirrored sequence.

Why does row 4 become 4321234?

The first loop prints 4 3 2, and the second loop prints 1 2 3 4, which together form 4321234.

How many digits does row i print?

Row i prints 2i - 1 digits — one more than the previous row.

How is this different from Program 36?

Program 36 is right-aligned with decreasing sequences. Program 37 builds a symmetric palindrome on each row with two inner loops.

How do I change the number of rows?

Replace 5 with rows in the outer loop bound — see Example 2.

What is the time complexity?

O(n²) for n rows because total digits printed are 1 + 3 + 5 + ... + (2n-1) = n².

How should I read rows safely?

Use a try/except ValueError around int(input()) or check the raw string with .isdigit() before converting so bad input does not crash the script.

What happens when rows is 1?

Only one row prints — a single digit 1.

Did you Know? 🔊

Each row is a palindrome: print i down to 2, then 1 up to i. Row i prints 2i - 1 digits — total digits across all rows = n².

Continue to Program 38

Move on to the next pattern in the Python number-pattern series.

Program 38 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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Python Number Pattern 36 — Right-Aligned Decreasing Triangle Python Number Pattern 38 — Sequential Decreasing-Width Triangle

Palindrome Number Triangle in Python

What You’ll Learn

Shape Rule

Outer Loop

Left Half

Right Half

Live Preview

O(n²)

Introduction

Why it matters?

i..2 desc

1..i asc

2i - 1

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 Fixed vs User Input vs Compact Demo

When This Pattern Shows Up

After Program 36

Symmetry drills

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

📈 User Input

Example 2 — User input rows

How It Works

⚡ Smaller Demo

Example 3 — Compact rows = 3

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop walks rows

Left half (descending)

Right half (ascending)

New line

Palindrome triangle complete

🔎 Worked Walkthrough — rows = 5

Use Cases

1. Teaching Nested Loops

2. Pattern Series Base

3. Console Formatting Drills

4. Padding character

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. Two Inner Loops Per Row

2. Call try/except ValueError

3. Keep newline outside inner loops

4. Trace halves on Paper

5. Dry-Run rows = 3

Common Pitfalls

1. Newline Inside an Inner Loop

2. Wrong Loop Order

3. Wrong Descending Bound

4. Including 1 Twice

5. Bare int(input())

Edge Cases

Single row

Empty pattern

rows < 1

Smallest triangle

Non-numeric input

Large row count

🎯 Practice Problems

1. Right-aligned decreasing

2. Next in series

3. Palindrome trace

Example 1 — Fixed `rows = 5`

Example 3 — Compact `rows = 3`

🔎 Worked Walkthrough — `rows = 5`

2. Call `try/except ValueError`

5. Bare `int(input())`

`rows < 1`