A104634 Triangle T(n,k) = (k-1-n)*(k-2-n)*(k+2*n)/6, 1<=k<=n.

1, 5, 2, 14, 8, 3, 30, 20, 11, 4, 55, 40, 26, 14, 5, 91, 70, 50, 32, 17, 6, 140, 112, 85, 60, 38, 20, 7, 204, 168, 133, 100, 70, 44, 23, 8, 285, 240, 196, 154, 115, 80, 50, 26, 9, 385, 330, 276, 224, 175, 130, 90, 56, 29, 10, 506, 440, 375, 312, 252, 196, 145, 100, 62, 32, 11, 650, 572, 495, 420, 348, 280, 217, 160, 110, 68, 35, 12, 819, 728, 638, 550, 465, 384

Offset: 1

Author

Gary W. Adamson, Mar 18 2005

Keywords

• nonn
• tabl
• easy

Examples

			The first few rows are:
1;
5, 2;
14, 8, 3;
30, 20, 11, 4;
55, 40, 26, 14, 5;
91, 70, 50, 32, 17, 6;
...
		

Links

• G. C. Greubel, Rows n=1..100 of triangle, flattened

Crossrefs

Cf. A000330 (column 1), A007290 (column 2), A051925 (column 3), A001296 (row sums), A104633, A000332.

Programs

Magma

[[(k-1-n)*(k-2-n)*(k+2*n)/6: k in [1..n]]: n in [1..20]]; // G. C. Greubel, Aug 12 2018

Maple

A104634 := proc(n,k) (k-1-n)*(k-2-n)*(k+2*n)/6 ; end proc:
seq(seq(A104634(n,k),k=1..n),n=1..15) ; # R. J. Mathar, Aug 31 2011

Mathematica

Table[(k-1-n)*(k-2-n)*(k+2*n)/6, {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Aug 12 2018 *)

PARI

for(n=1,20, for(k=1,n, print1((k-1-n)*(k-2-n)*(k+2*n)/6, ", "))) \\ G. C. Greubel, Aug 12 2018

Formula

The triangle is created by the matrix product A002260 * A004736, both infinite lower triangular matrices.

Extensions

Definition in closed form provided by R. J. Mathar, Aug 31 2011