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# User:L. Edson Jeffery/LA212329

A212329 (LaTeX version): Expansion of ${\frac {x(5+x)}{1-7x+7x^{2}-x^{3}}}$ .

## Sequence data

0, 5, 36, 217, 1272, 7421, 43260, 252145, 1469616, 8565557, 49923732, 290976841, 1695937320, 9884647085, 57611945196, 335787024097, 1957110199392, 11406874172261, 66484134834180, 387497934832825

## Offset

1, 2

 Table of differences re Table A182441.
 This is a sequence of differences between rows $k$ and $k+1$ of table A182441. That is if A182441$(k+1,0)$ $-$ A182441$(k,0)=1$ , $a(n)$ $=$ A182441$(k+1,n+1)$ $-$ A182441$(k,n+1)$ for $n=0$ to $3$ . The remainder of the sequence is a continuation using the recursive formula $D(n)=6D(n-1)-D(n-2)+6$ .
 It appears that for $n>0$ , $a(n)$ is divisible by A213005$(n)$ .
 It appears that if $p$ is a prime of the form $8r\pm 1$ , $a(p-1)\equiv 0{\pmod {p}}$ ; and that if $p$ is a prime of the form $8r\pm 3$ , $a(p+1)\equiv 0{\pmod {p}}$ .

## Formulas

$a(n)=7a(n-1)-7a(n-2)+a(n-3)$ .

nonn

## Author(s)

Kenneth J Ramsey, May 14 2012

## Missing %-fields

For links, references, programs, cross-references, extensions or other missing %-fields (if they exist), see A212329.

## Disclaimer

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