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A125786 Column 6 of table A125781. 5
1, 7, 39, 216, 1274, 8200, 58017, 451283, 3847960, 35818351, 362337006, 3965467281, 46749441514, 591291743032, 7993582141984, 115104783083605, 1759853074058289, 28485332959460764, 486811835886953020 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

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

FORMULA

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

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A099460 A092923 A164550 * A155589 A071082 A122884

Adjacent sequences:  A125783 A125784 A125785 * A125787 A125788 A125789

KEYWORD

nonn

AUTHOR

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

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Last modified February 16 02:51 EST 2012. Contains 205860 sequences.