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

0,2

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).

Formula

a(n) = (-1)^n * A077940(n). - 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 *)

Prog

(PARI) my(x='x+O('x^50)); Vec(1/(1+2*x-2*x^3)) \\ G. C. Greubel, Jun 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 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
(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

Crossrefs

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

Sequence in context: A237047 A021806 A077940 * A166880 A079088 A161661

Adjacent sequences: A077985 A077986 A077987 * A077989 A077990 A077991

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved