A130297 A130296^2.

1, 4, 1, 8, 2, 1, 13, 3, 2, 1, 19, 4, 3, 2, 1, 26, 5, 4, 3, 2, 1, 34, 6, 5, 4, 3, 2, 1, 43, 7, 6, 5, 4, 3, 2, 1, 53, 8, 7, 6, 5, 4, 3, 2, 1, 64, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Author

Gary W. Adamson, May 20 2007

Keywords

• nonn
• tabl

Comments

Left border = A034856: (1, 4, 8, 13, 19, 26, 34, ...).

Row sums = A028387: (1, 5, 11, 19, 29, 41, 55, ...).

Examples

			First few rows of the triangle:
   1;
   4, 1;
   8, 2, 1;
  13, 3, 2, 1;
  19, 4, 3, 2, 1;
  26, 5, 4, 3, 2, 1;
  ...
		

Crossrefs

Cf. A130296, A034856, A028387.

Programs

Python

from math import comb, isqrt
def A130297(n): return (a:=comb(r:=(m:=isqrt(k:=n<<1))+(k>m*(m+1))+1,2))+1-n+(a-1 if ((k2:=n-1<<1)==(m2:=isqrt(k2))*(m2+1)) else 0) # Chai Wah Wu, Nov 09 2024

Formula

Square of A130296 as an infinite lower triangular matrix.