A077965 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

N. Gogin and A. Mylläri, Padovan-like sequences and Bell polynomials, Proceedings of Applications of Computer Algebra ACA, 2013.

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

Formula

a(0)=1, a(1)=0, a(2)=-2, a(n) = -2*a(n-2)+a(n-3). - Harvey P. Dale, Jan 22 2015

a(n) = (-1)^n * A077967(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, Jan 22 2015 *)

Prog

(PARI) my(x='x+O('x^50)); Vec(1/(1+2*x^2-x^3)) \\ Altug Alkan, Feb 20 2018
(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. A077967.

Sequence in context: A127480 A141446 A339407 * A077967 A296188 A008312

Adjacent sequences: A077962 A077963 A077964 * A077966 A077967 A077968

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved