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A078061 Expansion of (1-x)/(1+2*x+x^3). 1
1, -3, 6, -13, 29, -64, 141, -311, 686, -1513, 3337, -7360, 16233, -35803, 78966, -174165, 384133, -847232, 1868629, -4121391, 9090014, -20048657, 44218705, -97527424, 215103505, -474425715, 1046378854, -2307861213, 5090148141, -11226675136, 24761211485, -54612571111, 120451817358 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..32.

Shanzhen Gao, Keh-Hsun Chen, Tackling Sequences From Prudent Self-Avoiding Walks, FCS'14, The 2014 International Conference on Foundations of Computer Science.

Index entries for linear recurrences with constant coefficients, signature (-2,0,-1).

FORMULA

a(n) = (-1)^n*sum{k=0..n, C(n-k,floor(k/2))*2^(n-k-floor(k/2))}. [Paul Barry, Oct 20 2009]

MATHEMATICA

CoefficientList[Series[(1-x)/(1+2x+x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[ {-2, 0, -1}, {1, -3, 6}, 40] (* Harvey P. Dale, Dec 15 2017 *)

PROG

(PARI) Vec((1-x)/(1+2*x+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

CROSSREFS

Sequence in context: A052933 A071014 A214260 * A018909 A093128 A005313

Adjacent sequences:  A078058 A078059 A078060 * A078062 A078063 A078064

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified March 1 02:21 EST 2021. Contains 341732 sequences. (Running on oeis4.)