A147617 Expansion of g.f.: 1/((1 - x - x^2 + x^5 - x^7)*(1 - x^2 + x^5 + x^6 - x^7)).

1, 1, 3, 4, 8, 10, 17, 24, 37, 55, 85, 132, 202, 317, 488, 761, 1171, 1818, 2802, 4333, 6688, 10334, 15964, 24661, 38115, 58886, 91011, 140619, 217317, 335783, 518882, 801765, 1238908, 1914362, 2958086, 4570887, 7062966, 10913848, 16864199

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1,-2,0,5,0,-2,-1,-1,2,1,-1).

Formula

G.f.: 1/(1 - x - 2*x^2 + x^3 + x^4 + 2*x^5 - 5*x^7 + 2*x^9 + x^10 + x^11 - 2*x^12 - x^13 + x^14).

G.f.: -1/(x^7*f(x)*f(1/x)), where f(x) = -1 + x + x^2 - x^5 + x^7. - G. C. Greubel, Oct 24 2022

Mathematica

f[x_]= -1+x+x^2-x^5+x^7;
CoefficientList[Series[-1/(x^7*f[x]*f[1/x]), {x, 0, 50}], x] (* G. C. Greubel, Oct 24 2022 *)

Prog

(PARI) Vec(1/(1 -x -2*x^2 +x^3 +x^4 +2*x^5 -5*x^7 +2*x^9 +x^10 +x^11 -2*x^12 - x^13 +x^14) + O(x^40)) \\ Jinyuan Wang, Mar 10 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x-x^2+x^5- x^7)*(1-x^2+x^5+x^6-x^7)) )); // G. C. Greubel, Oct 24 2022
(SageMath)
def A147617_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x-x^2+x^5-x^7)*(1-x^2+x^5+x^6-x^7)) ).list()
A147617_list(40) # G. C. Greubel, Oct 24 2022

Crossrefs

Cf. A147607, A147620, A147621.

Sequence in context: A212543 A355193 A238546 * A308910 A308959 A326451

Adjacent sequences: A147614 A147615 A147616 * A147618 A147619 A147620

Keyword

nonn,easy,less

Author

Roger L. Bagula, Nov 08 2008

Extensions

Definition corrected by N. J. A. Sloane, Nov 09 2008

Status

approved