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A114689 Expansion of (-1-4*x+x^2)/((1-x)*(x+1)*(x^2+2*x-1)); a Pellian-related sequence. 5
1, 6, 13, 36, 85, 210, 505, 1224, 2953, 7134, 17221, 41580, 100381, 242346, 585073, 1412496, 3410065, 8232630, 19875325, 47983284, 115841893, 279667074, 675176041, 1630019160, 3935214361, 9500447886, 22936110133, 55372668156, 133681446445, 322735561050 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Elements of odd index give match to A075848: 2*n^2 + 9 is a square. Generating floretion: - 1.5'i + 'j + 'k - .5i' + j' + k' + .5'ii' - .5'jj' - .5'kk' - 'ij' + 'ik' - 'ji' + .5'jk' + 2'ki' - .5'kj' + .5e

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

From Colin Barker, May 26 2016: (Start)

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

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

(End)

PROG

(PARI) Vec((-1-4*x+x^2)/((1-x)*(x+1)*(x^2+2*x-1)) + O(x^30)) \\ Colin Barker, May 26 2016

CROSSREFS

Cf. A100828, A111954, A113224, A114647, A114688, A114695, A114696, A114697, A000129, A005409.

Sequence in context: A041068 A037243 A107710 * A280532 A216508 A057451

Adjacent sequences:  A114686 A114687 A114688 * A114690 A114691 A114692

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Feb 18 2006

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.