A077967 Expansion of 1/(1+2*x^2+x^3).

1, 0, -2, -1, 4, 4, -7, -12, 10, 31, -8, -72, -15, 152, 102, -289, -356, 476, 1001, -596, -2478, 191, 5552, 2096, -11295, -9744, 20494, 30783, -31244, -82060, 31705, 195364, 18650, -422433, -232664, 826216, 887761, -1419768, -2601738, 1951775, 6623244, -1301812, -15198263, -4019620

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,-2,-1).

Formula

a(n) = (-1)^n * A077965(n). - G. C. Greubel, Jun 24 2019

Mathematica

CoefficientList[Series[1/(1+2x^2+x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[ {0, -2, -1}, {1, 0, -2}, 50] (* Harvey P. Dale, Nov 10 2017 *)

Prog

(PARI) my(x='x+O('x^50)); Vec(1/(1+2*x^2+x^3)) \\ G. C. Greubel, Jun 24 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+2*x^2+x^3) )); // G. C. Greubel, Jun 24 2019
(Sage) (1/(1+2*x^2+x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019
(GAP) a:=[1, 0, -2];; for n in [4..50] do a[n]:=-2*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jun 24 2019

Crossrefs

Cf. A077965.

Sequence in context: A141446 A339407 A077965 * A296188 A008312 A345442

Adjacent sequences: A077964 A077965 A077966 * A077968 A077969 A077970

Keyword

sign

Author

N. J. A. Sloane, Nov 17 2002

Status

approved