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

0,5

Links

Table of n, a(n) for n=0..65.

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]

Example

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, 28, 45, 60, 45, 18, 1;
...

Prog

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

Crossrefs

Cf. A007318, A103451, A131128 (row sums)

Sequence in context: A195408 A011491 A189089 * A140284 A143087 A144470

Adjacent sequences: A132044 A132045 A132046 * A132048 A132049 A132050

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Aug 08 2007

Extensions

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

Status

approved