0,2

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

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

a(n) = A125784(n+1) - A125783(n+1) for n>0:

A125784 begins: 1, 5, 21, 91, 433, 2307, 13804, 92433, 688611, ...;

A125783 begins: 1, 4, 14, 52, 217, 1033, 5604, 34416, 237328, ...;

term-by-term differences form 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.

Cf. A125781; other columns: A091352, A125782, A125783, A125784, A125785.

Sequence in context: A099460 A092923 A164550 this_sequence A155589 A071082 A122884

Adjacent sequences: A125783 A125784 A125785 this_sequence A125787 A125788 A125789

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 09 2006