A147593 Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).

1, 1, 1, 0, 2, 3, 5, 3, 6, 8, 16, 16, 24, 28, 50, 61, 91, 109, 170, 220, 327, 415, 607, 800, 1164, 1536, 2192, 2928, 4172, 5616, 7921, 10705, 15049, 20460, 28638, 39027, 54453, 74451, 103662, 141996, 197288, 270704, 375632, 516096, 715258, 983661, 1362091

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,3,-1,0,1,-1).

Formula

G.f.: -1/(x^4*f(x)*f(1/x)), where f(x) = -1 - x^3 + x^4.

G.f.: 1/((1+x^3-x^4)*(1-x-x^4)). - Colin Barker, Nov 04 2012

Mathematica

f[x_]= x^4-x^3-1; CoefficientList[Series[-1/(x^4*f[x]*f[1/x]), {x, 0, 50}], x]

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1+x^3-x^4)*(1-x-x^4)) )); // G. C. Greubel, Oct 25 2022
(SageMath)
def A147593_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x^3-x^4)*(1-x-x^4)) ).list()
A147593_list(50) # G. C. Greubel, Oct 25 2022

Crossrefs

Cf. A147598, A147605, A147606, A147607, A147617, A147620.

Sequence in context: A185191 A103781 A095244 * A108396 A239476 A117367

Adjacent sequences: A147590 A147591 A147592 * A147594 A147595 A147596

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 08 2008

Extensions

Edited by Joerg Arndt and Colin Barker, Nov 04 2012.

Status

approved