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

1,3

Links

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

Formula

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

Example

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;

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 *)

Prog

(Magma) [(k-1)*(3*n-k-1): k in [1..n], n in [1..12]]; // 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

Crossrefs

Cf. A255211 (row sums).

Sequence in context: A216473 A378390 A198433 * A077911 A057381 A144091

Adjacent sequences: A141431 A141432 A141433 * A141435 A141436 A141437

Keyword

nonn,easy,tabl

Author

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

Status

approved