A131060 3*A007318 - 2*A000012 as infinite lower triangular matrices.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 10, 16, 10, 1, 1, 13, 28, 28, 13, 1, 1, 16, 43, 58, 43, 16, 1, 1, 19, 61, 103, 103, 61, 19, 1, 1, 22, 82, 166, 208, 166, 82, 22, 1, 1, 25, 106, 250, 376, 376, 250, 106, 25, 1, 1, 28, 133, 358, 628, 754, 628, 358, 133, 28, 1

Offset

0,5

Comments

Row sums = A097813: (1, 2, 6, 16, 38, 84, 178, ...).

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n,k) = 3*binomial(n,k) - 2. - Roger L. Bagula, Aug 20 2008

Example

First few rows of the triangle:
  1;
  1,  1;
  1,  4,  1;
  1,  7,  7,  1;
  1, 10, 16, 10,  1;
  1, 13, 28, 28, 13,  1;
  1, 16, 43, 58, 43, 16,  1;
  ...

Maple

A131060:= (n, k) -> 3*binomial(n, k)-2; seq(seq(A131060(n, k), k = 0..n), n = 0.. 10); # G. C. Greubel, Mar 12 2020

Mathematica

T[n_, k_] = 3*Binomial[n, k] -2; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* Roger L. Bagula, Aug 20 2008 *)

Prog

(Magma) [3*Binomial(n, k) -2: k in [0..n], n in [0..10]]; // G. C. Greubel, Mar 12 2020
(Sage) [[3*binomial(n, k) -2 for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 12 2020

Crossrefs

Cf. A109128, A123203, A131061, A131063, A131064, A131065, A131066, A131067, A131068.

Sequence in context: A152236 A296180 A157172 * A350512 A124376 A047671

Adjacent sequences: A131057 A131058 A131059 * A131061 A131062 A131063

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 13 2007

Extensions

More terms from Roger L. Bagula, Aug 20 2008

Status

approved