A078036 Expansion of (1-x)/(1+2*x^2+x^3).

1, -1, -2, 1, 5, 0, -11, -5, 22, 21, -39, -64, 57, 167, -50, -391, -67, 832, 525, -1597, -1882, 2669, 5361, -3456, -13391, 1551, 30238, 10289, -62027, -50816, 113765, 163659, -176714, -441083, 189769, 1058880, 61545, -2307529, -1181970, 4553513, 4671469, -7925056, -13896451, 11178643

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1-x)/(1+2*x^2+x^3).

a(0)=1, a(1)=-1, a(2)=-2, a(n)=-2*a(n-2)-a(n-3). - Harvey P. Dale, Dec 18 2012

a(n)=A077967(n)-A077967(n-1). - R. J. Mathar, Mar 19 2025

Mathematica

CoefficientList[Series[(1-x)/(1+2x^2+x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, -2, -1}, {1, -1, -2}, 50] (* Harvey P. Dale, Dec 18 2012 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, -2, 0]^n*[1; -1; -2])[1, 1] \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Cf. A077967.

Sequence in context: A338554 A317301 A131915 * A395538 A369865 A175178

Adjacent sequences: A078033 A078034 A078035 * A078037 A078038 A078039

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved