A077988 Expansion of 1/(1+2*x-2*x^3).

1, -2, 4, -6, 8, -8, 4, 8, -32, 72, -128, 192, -240, 224, -64, -352, 1152, -2432, 4160, -6016, 7168, -6016, 0, 14336, -40704, 81408, -134144, 186880, -210944, 153600, 66560, -555008, 1417216, -2701312, 4292608, -5750784, 6098944, -3612672, -4276224, 20750336, -48726016, 88899584

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
• J. Pan, Multiple Binomial Transforms and Families of Integer Sequences , J. Int. Seq. 13 (2010), 10.4.2, T^(-1).
• Index entries for linear recurrences with constant coefficients, signature (-2, 0, 2).

Crossrefs

Cf. A000073, A001590, A000213, A077940, A135491.

Programs

GAP

a:=[1,-2,4];; for n in [4..50] do a[n]:=-2*a[n-1]+2*a[n-3]; od; a; # G. C. Greubel, Jun 25 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+2*x-2*x^3) )); // G. C. Greubel, Jun 25 2019

Mathematica

LinearRecurrence[{-2, 0, 2}, {1, -2, 4}, 50] (* Vladimir Joseph Stephan Orlovsky, May 25 2011 *)
CoefficientList[Series[1/(1+2x-2x^3),{x,0,50}],x] (* Harvey P. Dale, May 21 2024 *)

PARI

my(x='x+O('x^50)); Vec(1/(1+2*x-2*x^3)) \\ G. C. Greubel, Jun 25 2019

Sage

(1/(1+2*x-2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 25 2019

Formula

a(n) = (-1)^n * A077940(n). - G. C. Greubel, Jun 25 2019