A089076 Expansion of -x - x^3*(2 -2*x^4 +x^5)/((1-x^2)*(1+x+x^4)).

-1, 0, -2, 2, -4, 4, -6, 7, -11, 14, -20, 26, -37, 50, -70, 95, -132, 181, -251, 345, -477, 657, -908, 1252, -1729, 2385, -3293, 4544, -6273, 8657, -11950, 16493, -22766, 31422, -43372, 59864, -82630, 114051, -157423, 217286, -299916, 413966, -571389, 788674, -1088590, 1502555, -2073944, 2862617

Offset

1,3

Comments

The definition and terms don't appear to match. Something is wrong. - Charles R Greathouse IV, May 27 2026

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: -x - x^3*(2 -2*x^4 +x^5)/((1-x^2)*(1+x+x^4)). [does not seem to match terms]

Mathematica

Rest@CoefficientList[Series[-x -x^3*(2-2*x^4+x^5)/((1-x^2)*(1+x-x^4)), {x, 0, 50}], x] (* G. C. Greubel, Feb 19 2021 *)
LinearRecurrence[{-1, 1, 1, 1, 0, -1}, {-1, 0, -2, 2, -4, 4, -6, 7}, 50] (* Harvey P. Dale, Aug 11 2021 *)

Prog

(SageMath)
def A089076_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( -x -x^3*(2-2*x^4+x^5)/((1-x^2)*(1+x-x^4)) ).list()
a=A089076_list(51); a[1:] # G. C. Greubel, Feb 19 2021
(Magma)
R<x>:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( -x -x^3*(2-2*x^4+x^5)/((1-x^2)*(1+x-x^4)) )); // G. C. Greubel, Feb 19 2021
(PARI) a(n)=if(n>2, ([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -1, 0, 1, 1, 1, -1]^(n-3)*[-2; 2; -4; 4; -6; 7])[1, 1], n-2) \\ Charles R Greathouse IV, May 27 2026

Crossrefs

Cf. A089074, A089075, A089077.

Sequence in context: A027188 A363213 A393986 * A123067 A218897 A218064

Adjacent sequences: A089073 A089074 A089075 * A089077 A089078 A089079

Keyword

sign,uned

Author

Roger L. Bagula, Dec 04 2003

Extensions

Edited by G. C. Greubel, Feb 19 2021

Status

approved