A125784 Column 4 of table A125781.

1, 5, 21, 91, 433, 2307, 13804, 92433, 688611, 5670713, 51291468, 506502769, 5430460072, 62894124926, 783259655434, 10445143907067, 148592182641759, 2247301621235992, 36021020633412788, 610161098104988668

Offset

0,2

Comments

Column k of triangle A091351 = row sums of matrix power A091351^k for k>=0.

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} [A091351^2](n+1,k+1) where A091351^2 is the matrix square of A091351.

Example

a(n) = A125783(n) + A125786(n-1) for n>0:
A125783 begins: 1, 4, 14, 52, 217, 1033, 5604, 34416, 237328, ...
and A125786 begins: 1, 7, 39, 216, 1274, 8200, 58017, 451283, ...
term-by-term addition forms this sequence.
This sequence can also be derived from the matrix square A091351^2:
1;
2, [1];
4, [4, 1];
9, [14, 6, 1];
24, [52, 30, 8, 1];
77, [217, 153, 52, 10, 1];
295, [1033, 845, 336, 80, 12, 1];
1329, [5604, 5152, 2294, 625, 114, 14, 1]; ...
The terms enclosed in square barackets sum to equal this sequence.

Crossrefs

Cf. A091351; other columns: A091352, A125782, A125783, A125785, A125786.

Sequence in context: A164037 A218961 A168444 * A218964 A154964 A007287

Adjacent sequences: A125781 A125782 A125783 * A125785 A125786 A125787

Keyword

nonn

Author

Paul D. Hanna, Dec 09 2006

Status

approved