A124314 Expansion of -1/(1 + x + x^2 + x^3 + x^4 - x^5).

-1, 1, 0, 0, 0, -2, 3, -1, 0, 0, -4, 8, -5, 1, 0, -8, 20, -18, 7, -1, -16, 48, -56, 32, -9, -31, 112, -160, 120, -50, -53, 255, -432, 400, -220, -56, 563, -1119, 1232, -840, 108, 1182, -2801, 3583, -2912, 1056, 2256, -6784, 9967, -9407, 5024

Offset: 0

Author

Artur Jasinski, Oct 25 2006

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,1).

Crossrefs

Cf. A124312, A124313.

Programs

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (-1+x)/(1-2*x^5+x^6) )); // G. C. Greubel, Aug 25 2023

Mathematica

CoefficientList[Series[1/(-1-x-x^2-x^3-x^4+x^5), {x,0,50}], x]
LinearRecurrence[{-1,-1,-1,-1,1}, {-1,1,0,0,0}, 60] (* G. C. Greubel, Aug 25 2023 *)

PARI

Vec(1/(-1-x-x^2-x^3-x^4+x^5)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

SageMath

def A124314_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (-1+x)/(1-2*x^5+x^6) ).list()
A124314_list(60) # G. C. Greubel, Aug 25 2023