A141434 Triangle T(n, k) = (k-1)*(3*n-k-1), read by rows.

0, 0, 3, 0, 6, 10, 0, 9, 16, 21, 0, 12, 22, 30, 36, 0, 15, 28, 39, 48, 55, 0, 18, 34, 48, 60, 70, 78, 0, 21, 40, 57, 72, 85, 96, 105, 0, 24, 46, 66, 84, 100, 114, 126, 136, 0, 27, 52, 75, 96, 115, 132, 147, 160, 171

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Aug 06 2008

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins as:
  0;
  0,  3;
  0,  6, 10;
  0,  9, 16, 21;
  0, 12, 22, 30, 36;
  0, 15, 28, 39, 48,  55;
  0, 18, 34, 48, 60,  70,  78;
  0, 21, 40, 57, 72,  85,  96, 105;
  0, 24, 46, 66, 84, 100, 114, 126, 136;
  0, 27, 52, 75, 96, 115, 132, 147, 160, 171;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A255211 (row sums).

Programs

Magma

[(k-1)*(3*n-k-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 01 2021

Maple

A141434:= (n,k) -> (k-1)*(3*n-k-1); seq(seq(A141434(n,k), k=1..n), n=1..12); # G. C. Greubel, Apr 01 2021

Mathematica

Table[(k-1)*(3*n-k-1), {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 01 2021 *)

Sage

flatten([[(k-1)*(3*n-k-1) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 01 2021

Formula

Sum_{k=1..n} T(n,k) = (n-1)*n*(7*n-5)/6. - R. J. Mathar, Sep 07 2011