A077981 Expansion of 1/(1+2*x-2*x^2-2*x^3).

1, -2, 6, -14, 36, -88, 220, -544, 1352, -3352, 8320, -20640, 51216, -127072, 315296, -782304, 1941056, -4816128, 11949760, -29649664, 73566592, -182532992, 452899840, -1123732480, 2788198656, -6918062592, 17165057536, -42589842944, 105673675776, -262196922368

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,2,2).

Crossrefs

Cf. A077937.

Programs

GAP

a:=[1,-2,6];; for n in [4..30] do a[n]:=-2*a[n-1]+2*a[n-2]+ 2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1+2*x-2*x^2-2*x^3) )); // G. C. Greubel, Jun 25 2019

Mathematica

LinearRecurrence[{-2,2,2}, {1,-2,6}, 30] (* or *) CoefficientList[ Series[1/(1+2*x-2*x^2-2*x^3), {x,0,30}], x] (* G. C. Greubel, Jun 25 2019 *)

PARI

Vec(1/(1+2*x-2*x^2-2*x^3) + O(x^30)) \\ Michel Marcus, Jun 19 2015

Sage

(1/(1+2*x-2*x^2-2*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019

Formula

a(n) = (-1)^n * A077937(n). - Ivan Neretin, Jun 19 2015