A147592 Expansion of 1/(1 + x - x^2 - 3*x^3 - x^4 + x^5 + x^6).
1, -1, 2, 0, 0, 4, -2, 5, 3, 0, 12, 0, 12, 16, 5, 35, 18, 36, 64, 40, 110, 105, 135, 240, 216, 384, 472, 560, 905, 999, 1458, 1960, 2368, 3500, 4302, 5805, 7947, 9936, 13860, 17920, 23588, 32096, 41229, 55755, 73570, 96460, 129920, 169680, 226206, 300369
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-1,1,3,1,-1,-1).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1+x-x^3)*(1-x^2-x^3)) )); // G. C. Greubel, Oct 25 2022 -
Mathematica
f[x_]= x^3-x-1; CoefficientList[Series[-1/(x^3*f[x]*f[1/x]), {x,0,60}], x] LinearRecurrence[{-1,1,3,1,-1,-1},{1,-1,2,0,0,4},60] (* Harvey P. Dale, Sep 23 2020 *) -
SageMath
def A147592_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( 1/((1+x-x^3)*(1-x^2-x^3)) ).list() A147592_list(60) # G. C. Greubel, Oct 25 2022
Formula
G.f.: -1/(x^3*f(x)*f(1/x)), where f(x) = -1 - x + x^3.
G.f.: 1/((1+x-x^3)*(1-x^2-x^3)). - Colin Barker, Nov 04 2012
Extensions
Edited by Joerg Arndt and Colin Barker, Nov 04 2012