A078061 Expansion of (1-x)/(1+2*x+x^3).

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

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• 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).

Programs

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 *)

PARI

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

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]

(-1)^n*a(n) = A008998(n)+A008998(n-1). - R. J. Mathar, Jul 08 2022