JavaScript Sequential Number Triangle Pattern (Narrowing)
Beginner
5 min read
Updated: Sep 2026
3 programs
Live preview
Definition
What Is This Pattern?
A sequential decreasing-width triangle prints one continuous sequence — row 1 has n values, row 2 has n-1, and so on down to a single number.
Remember
Rule: k = 1; for i = 1..rows
print (rows - i + 1) values of k with padStart(3)
1 2 3 4 5
6 7 8 9
10 11 12
13 14
15 ← rows = 5
After Program 37’s palindrome rows, this pattern focuses on a shared counter and shrinking inner bounds.
Approach
How to Solve It
Walk i from 1 to rows; on each row append rows - i + 1 values from counter k.
Method
Idea
Best for
Counter + shrink
Inner j = rows..i; padStart(3) and k++
Learning, interviews
prompt rows
Same loops; read rows at runtime
Interactive practice
Custom start k
Same shape; initialize k to any start value
Sequence variants
Pseudocode
Pseudocode
k = 1
for i from 1 to rows:
line = ""
for j from rows down to i:
line += pad(k, width 3)
k += 1
print line
Cheat sheet
Goal
Pattern
Set rows / counter
const rows = 5; let k = 1;
Outer loop
for (let i = 1; i <= rows; i++)
Inner loop
for (let j = rows; j >= i; j--)
Number cell
line += String(k).padStart(3, " "); k += 1;
End row
console.log(line);
Values per row
rows - i + 1
Total values
n(n+1)/2 for n rows
Printing Numbers vs Starting a New Line
API
Effect
Use for
line += String(k).padStart(3, " ")
Stays on the same row
Each cell
console.log(line)
Ends the line
After the inner loop
Build the row with +=, then break once with console.log. Putting console.log inside the inner loop prints one cell per line.
Try it
Live Preview
Change the row count and the sequential triangle updates instantly.
Whole numbers from 1 to 9. Tap a chip or type a value — the preview redraws as you go.
Live resultrows = 5 · values = 15
1 2 3 4 5
6 7 8 9
10 11 12
13 14
15
Trace
Worked Walkthrough — rows = 3
Trace each outer i, how many values the inner loop prints, the k range, and the printed row.
i
Inner runs
k range
Printed row
1
3
1..3
1 2 3
2
2
4..5
4 5
3
1
6
6
Inner runs = rows - i + 1. Counter k never resets between rows. Total values = 6 = 3×4/2.
Code
JavaScript Programs
Three complete programs: fixed rows = 5, prompt rows, and custom start k = 10. Use View Output for sample results, or Try It Yourself to edit and run in the playground.
Example 1 — Fixed rows = 5
Hard-coded height — shrinking inner loop, continuous k, and padStart(3).
JavaScript
const rows = 5;
let k = 1;
for (let i = 1; i <= rows; i++) {
let line = "";
for (let j = rows; j >= i; j--) {
line += String(k).padStart(3, " ");
k += 1;
}
console.log(line);
}
1. Counter.k starts at 1 and increments after every cell — the sequence never resets between rows.
2. Shrinking inner loop.j runs from rows down to i, so row 1 prints 5 values, row 2 prints 4, and so on.
3. Alignment.padStart(3, " ") keeps two-digit numbers (10–15) lined up with single digits.
Example 2 — prompt Rows
Read rows at runtime with prompt and parseInt.
JavaScript
const rows = parseInt(prompt("Enter rows:"), 10);
if (!Number.isFinite(rows) || rows < 1) {
console.log("Please enter a positive integer.");
} else {
let k = 1;
for (let i = 1; i <= rows; i++) {
let line = "";
for (let j = rows; j >= i; j--) {
line += String(k).padStart(3, " ");
k += 1;
}
console.log(line);
}
}
1. Prompt and validate. Parse the answer; reject non-positive or non-numeric input.
2. Same shape. The inner bound still uses rows and i — only the outer limit changes.
3. Counter restarts at 1. Each run begins a fresh sequence from k = 1.
Example 3 — Custom Start k = 10
Same shrinking triangle, but the continuous sequence begins at 10 instead of 1.
JavaScript
const rows = 5;
let k = 10;
for (let i = 1; i <= rows; i++) {
let line = "";
for (let j = rows; j >= i; j--) {
line += String(k).padStart(3, " ");
k += 1;
}
console.log(line);
}
1. Only k changes. Loops and padStart match Example 1 — just initialize k = 10.
2. Same total count. Still 15 values for rows = 5; they just run from 10 through 24.
3. Try other starts. Set k = 100 or any integer once you understand the default.
Edge Cases & Pitfalls
Check these before calling the solution done.
reset k
Broken sequence
If you set k = 1 inside the outer loop, every row restarts at 1 instead of continuing.
inner bound
Wrong width
Use j >= i, not j >= 1. Stopping at 1 prints a full rectangle of n² values.
log inside
Vertical cells
If console.log is inside the inner loop, each number lands on its own line.
no padStart
Crooked columns
Without padStart(3), single-digit and two-digit cells misalign once k ≥ 10.
rows = 1
Single cell
Output is one padded value — the starting k.
NaN input
Validate parseInt
Letters or empty prompt yield NaN — check Number.isFinite(rows) && rows >= 1.
Analysis
Time and Space Complexity
Program
Time
Extra space
Examples 1–3
O(n²)
O(n) for the current line string
Values per pattern = n + (n-1) + … + 1 = n(n+1)/2 → O(n²).
Remember
Key Takeaways
Rule: print rows - i + 1 consecutive values of k on each row.
Shared counter: initialize k once; never reset it inside the outer loop.
Write vs log:line += padStart(k) builds; console.log(line) breaks.
Complexity: total values = n(n+1)/2 → O(n²).
One line: shrink the inner count each row while a shared k keeps counting upward.
Frequently Asked Questions
Row lengths are 5, 4, 3, 2, and 1. Their sum is 5+4+3+2+1 = 15, which equals n(n+1)/2.
padStart(3, " ") right-aligns each integer in a 3-character field so columns stay neat when numbers reach two digits.
Each row prints a different count of values, but the sequence must continue globally (1, 2, 3, …). k stores the next value and increments after every append.
Yes. Initialize k with your starting value instead of 1 — see Example 3 with k = 10.
Program 37 builds a palindrome on each row (4321234). Program 38 appends one continuous ascending sequence with shrinking row widths.
Replace 5 with rows in the outer loop bound — see Example 2.
O(n²) where n is the number of rows. Total appended values equal 1+2+…+n = n(n+1)/2.
Use parseInt with Number.isFinite so bad input does not produce NaN.
Only one row prints — a single padded 1.
🤔
Did you know?
Row i appends 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.
