A077993 Expansion of 1/(1+2*x+2*x^2+2*x^3).

1, -2, 2, -2, 4, -8, 12, -16, 24, -40, 64, -96, 144, -224, 352, -544, 832, -1280, 1984, -3072, 4736, -7296, 11264, -17408, 26880, -41472, 64000, -98816, 152576, -235520, 363520, -561152, 866304, -1337344, 2064384, -3186688, 4919296, -7593984, 11722752, -18096128, 27934720, -43122688

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign

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. A077943.

Programs

GAP

a:=[1,-2,2];; for n in [4..50] do a[n]:=-2*(a[n-1]+a[n-2]+a[n-3]); od; a; # G. C. Greubel, Jun 27 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+2*x+2*x^2+2*x^3) )); // G. C. Greubel, Jun 27 2019

Mathematica

LinearRecurrence[{-2,-2,-2}, {1,-2,2}, 50] (* or *) CoefficientList[ Series[1/(1+2*x+2*x^2+2*x^3), {x,0,50}], x] (* G. C. Greubel, Jun 27 2019 *)

PARI

my(x='x+O('x^50)); Vec(1/(1+2*x+2*x^2+2*x^3)) \\ G. C. Greubel, Jun 27 2019

Sage

(1/(1+2*x+2*x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 27 2019

Formula

a(n) = (-1)^n * A077943(n). - R. J. Mathar, Aug 04 2008