A131818 A130296 + A002260 - A000012. Triangle read by rows: row n consists of n, 2, 3, 4, ..., n.

1, 2, 2, 3, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Offset: 1

Author

Gary W. Adamson, Jul 18 2007

Keywords

• nonn
• tabl

Comments

Row sums = A034856; (1, 4, 8, 13, 19, 26, 34, ...).

Examples

			First few rows of the triangle:
  1;
  2, 2;
  3, 2, 3;
  4, 2, 3, 4;
  5, 2, 3, 4, 5;
  6, 2, 3, 4, 5, 6;
  7, 2, 3, 4, 5, 6, 7;
  ...
		

Crossrefs

Cf. A130296, A002260, A034856.

Programs

Mathematica

Table[Join[{n},Range[2,n]],{n,15}]//Flatten (* Harvey P. Dale, Feb 24 2021 *)

PARI

t(n, k) = if (k==1, n, k); \\ Michel Marcus, Feb 12 2014

Python

from math import isqrt, comb
def A131818(n):
    y = (m:=isqrt(k:=n-1<<1))+(k>m*(m+1))
    return n-comb(y,2) # Chai Wah Wu, Jul 07 2025

Formula

A130296 + A002260 - A000012 as infinite lower triangular matrices.

T(n, 1) = n, T(n, k) = k for k > 1. - Michel Marcus, Feb 12 2014

Extensions

More terms from Michel Marcus, Feb 12 2014