A132047 3*A007318 - 2*A103451 as infinite lower triangular matrices.

1, 1, 1, 1, 6, 1, 1, 9, 9, 1, 1, 12, 18, 12, 1, 1, 15, 30, 30, 15, 1, 1, 18, 45, 60, 45, 18, 1, 1, 21, 63, 105, 105, 63, 21, 1, 1, 24, 84, 168, 210, 168, 84, 24, 1, 1, 27, 108, 252, 378, 378, 252, 108, 27, 1, 1, 30, 135, 360, 630, 756, 630, 360, 135, 30, 1

Offset: 0

Author

Gary W. Adamson, Aug 08 2007

Keywords

• nonn
• tabl
• easy

Examples

			First few rows of the triangle are:
  1;
  1, 1;
  1, 6, 1;
  1, 9, 9, 1;
  1, 12, 18, 12, 1;
  1, 15, 30, 30, 15, 1;
  1, 18, 45, 60, 45, 18, 1;
  ...
		

Crossrefs

Cf. A007318, A103451, A131128 (row sums).

Programs

PARI

T(n, k) = my(bnk = binomial(n, k)); 3*bnk - 2*(bnk==1); \\ Michel Marcus, Jun 16 2022

Formula

a(n) = 3*A007318(n) - 2*A103451(n).

T(n,k) = 3*C(n,k)-2*(C(n,k-n)+C(n,-k)-C(0,n+k)), 0<=k<=n. [Eric Werley, Jul 01 2011]

Extensions

Corrected and extended by Roger L. Bagula, Nov 02 2008