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

Author

Gary W. Adamson, Jun 13 2007

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
  ...
		

Links

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

Crossrefs

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

Programs

Magma

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

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 *)

Sage

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

Formula

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

Extensions

More terms from Roger L. Bagula, Aug 20 2008