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A114697 Expansion of (1+x+x^2)/((x-1)*(x+1)*(x^2+2*x-1)); a Pellian-related sequence. 5
1, 3, 9, 22, 55, 133, 323, 780, 1885, 4551, 10989, 26530, 64051, 154633, 373319, 901272, 2175865, 5253003, 12681873, 30616750, 73915375, 178447501, 430810379, 1040068260, 2510946901, 6061962063, 14634871029, 35331704122, 85298279275, 205928262673 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Generating floretion: (- .5'j + .5'k - .5j' + .5k' + 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki')*('i + 'j + i')

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1).

FORMULA

a(n+2) - 2*a(n+1) + a(n) = A111955(n+2).

a(2*n) = A216134(2*n+1). a(2*n+1) = A006452(2*n+3)-1. Lim a(n+1)/a(n) = A014176. - Raphie Frank, Oct 01 2012

a(n) = A078343(n+2)/2 - A010694(n)/4. - R. J. Mathar, Oct 02 2012

From Colin Barker, May 26 2016: (Start)

a(n) = (2*(-3+(-1)^n)+(6-5*sqrt(2))*(1-sqrt(2))^n+(1+sqrt(2))^n*(6+5*sqrt(2)))/8.

a(n) = 2*a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4) for n>3.

(End)

PROG

(PARI) Vec((x^2+x+1)/((x-1)*(x+1)*(x^2+2*x-1)) + O(x^100)) \\ Colin Barker, Jun 24 2015

CROSSREFS

Cf. A100828, A111954, A113224, A114647, A114688, A114689, A114695, A116699, A000129, A005409.

Sequence in context: A202882 A054442 A192663 * A032284 A203454 A197666

Adjacent sequences:  A114694 A114695 A114696 * A114698 A114699 A114700

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Feb 18 2006

STATUS

approved

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Last modified November 18 12:21 EST 2017. Contains 294891 sequences.