The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A125784

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A125784

Column 4 of table A125781.
(history; published version)

#3 by Russ Cox at Fri Mar 30 18:37:02 EDT 2012

AUTHOR

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

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#2 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

KEYWORD

nonn,new

nonn

AUTHOR

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

#1 by N. J. A. Sloane at Fri Jan 12 03:00:00 EST 2007

NAME

Column 4 of table A125781.

DATA

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.

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.

KEYWORD

nonn

AUTHOR

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

STATUS

approved