cp's OEIS Frontend

A125784 Column 4 of table A125781.

%I A125784 #3 Mar 30 2012 18:37:02
%S A125784 1,5,21,91,433,2307,13804,92433,688611,5670713,51291468,506502769,
%T A125784 5430460072,62894124926,783259655434,10445143907067,148592182641759,
%U A125784 2247301621235992,36021020633412788,610161098104988668
%N A125784 Column 4 of table A125781.
%C A125784 Column k of triangle A091351 = row sums of matrix power A091351^k for k>=0.
%F A125784 a(n) = Sum_{k=0..n} [A091351^2](n+1,k+1) where A091351^2 is the matrix square of A091351.
%e A125784 a(n) = A125783(n) + A125786(n-1) for n>0:
%e A125784 A125783 begins: 1, 4, 14, 52, 217, 1033, 5604, 34416, 237328, ...
%e A125784 and A125786 begins: 1, 7, 39, 216, 1274, 8200, 58017, 451283, ...
%e A125784 term-by-term addition forms this sequence.
%e A125784 This sequence can also be derived from the matrix square A091351^2:
%e A125784 1;
%e A125784 2, [1];
%e A125784 4, [4, 1];
%e A125784 9, [14, 6, 1];
%e A125784 24, [52, 30, 8, 1];
%e A125784 77, [217, 153, 52, 10, 1];
%e A125784 295, [1033, 845, 336, 80, 12, 1];
%e A125784 1329, [5604, 5152, 2294, 625, 114, 14, 1]; ...
%e A125784 The terms enclosed in square barackets sum to equal this sequence.
%Y A125784 Cf. A091351; other columns: A091352, A125782, A125783, A125785, A125786.
%K A125784 nonn
%O A125784 0,2
%A A125784 _Paul D. Hanna_, Dec 09 2006