A077869 Expansion of (1-x)^(-1)/(1-x+x^3).

1, 2, 3, 3, 2, 0, -2, -3, -2, 1, 5, 8, 8, 4, -3, -10, -13, -9, 2, 16, 26, 25, 10, -15, -39, -48, -32, 8, 57, 90, 83, 27, -62, -144, -170, -107, 38, 209, 317, 280, 72, -244, -523, -594, -349, 175, 770, 1120, 946, 177, -942, -1887, -2063, -1120, 768, 2832, 3953, 3186, 355, -3597, -6782, -7136, -3538, 3245

Offset

0,2

Links

Table of n, a(n) for n=0..63.

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

Formula

a(n) = Sum_{k=0..floor((n+1)/2)} (-1)^k*binomial(n+1-2k,k+1), n>=0. - Taras Goy, Apr 15 2020

From Wesley Ivan Hurt, Jan 25 2022: (Start)

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

a(n) = 2*a(n-1)-a(n-2)-a(n-3)+a(n-4). (End)

Mathematica

CoefficientList[Series[(1/(1-x))/(1-x+x^3), {x, 0, 70}], x] (* Harvey P. Dale, Mar 20 2013 *)

Crossrefs

Sequence in context: A279645 A198197 A203400 * A076585 A323186 A022906

Adjacent sequences: A077866 A077867 A077868 * A077870 A077871 A077872

Keyword

sign

Author

N. J. A. Sloane, Nov 17 2002

Status

approved