A078056 Expansion of (1-x)/(1+2*x-x^2-x^3).

1, -3, 7, -16, 36, -81, 182, -409, 919, -2065, 4640, -10426, 23427, -52640, 118281, -265775, 597191, -1341876, 3015168, -6775021, 15223334, -34206521, 76861355, -172705897, 388066628, -871977798, 1959316327, -4402543824, 9892426177, -22228079851, 49946042055, -112227737784

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Absolute values of pairwise sums are in A052534.

Links

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

Crossrefs

Cf. A052534.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!((1-x)/(1+2*x-x^2-x^3))); // Vincenzo Librandi, Feb 21 2020

Mathematica

CoefficientList[Series[(1-x)/(1+2*x-x^2-x^3),{x,0,60}],x] (* Harvey P. Dale, Feb 20 2020 *)

PARI

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

Formula

G.f.: (1-x)/(1+2*x-x^2-x^3).

a(n) = -2*a(n-1) + a(n-2) + a(n-3). - Wesley Ivan Hurt, Dec 29 2023

a(n) = (-1)^n*(A106805(n)+A106805(n+1)). -R. J. Mathar, Mar 19 2025