A125786 - OEIS

%I #3 Mar 30 2012 18:37:02

%S 1,7,39,216,1274,8200,58017,451283,3847960,35818351,362337006,

%T 3965467281,46749441514,591291743032,7993582141984,115104783083605,

%U 1759853074058289,28485332959460764,486811835886953020

%N Column 6 of table A125781.

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

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

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

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

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

%e term-by-term differences form this sequence.

%e This sequence can also be derived from the matrix square A091351^2:

%e 1;

%e 2, 1;

%e 4, 4, [1];

%e 9, 14, [6, 1];

%e 24, 52, [30, 8, 1];

%e 77, 217, [153, 52, 10, 1];

%e 295, 1033, [845, 336, 80, 12, 1];

%e 1329, 5604, [5152, 2294, 625, 114, 14, 1]; ...

%e the terms enclosed in square barackets sum to equal this sequence.

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 09 2006