A147598 Expansion of g.f. 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)).

1, 1, 3, 2, 4, 3, 6, 9, 14, 23, 29, 45, 57, 88, 123, 184, 267, 382, 556, 787, 1149, 1643, 2392, 3444, 4978, 7184, 10348, 14956, 21550, 31152, 44924, 64881, 93611, 135101, 195000, 281382, 406201, 586164, 846121, 1221064, 1762399, 2543555, 3671003

Offset: 0

Author

Roger L. Bagula, Nov 08 2008

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-3,-1,5,-1,-3,2,1,-1).

Crossrefs

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

Programs

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)) )); // G. C. Greubel, Oct 25 2022

Mathematica

f[x_]= x^5 -x^4 -x^3 +x^2 -1;
CoefficientList[Series[-1/(x^5*f[x]*f[1/x]), {x,0,50}],x]

SageMath

def A147598_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)) ).list()
A147598_list(50) # G. C. Greubel, Oct 25 2022

Formula

G.f.: -1/(x^5*f(x)*f(1/x)), where f(x) = -1 +x^2 -x^3 -x^4 +x^5.

G.f.: 1/((x^5-x^4-x^3+x^2-1)*(x^5-x^3+x^2+x-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

Extensions

Better name (using g.f.) from Joerg Arndt, Apr 06 2018