A147622 Expansion of g.f.: 1/(1 - x - 2*x^2 + x^3 + x^4 + 2*x^7 - 5*x^9 + 2*x^11 + x^14 + x^15 - 2*x^16 - x^17 + x^18).

1, 1, 3, 4, 8, 12, 21, 31, 51, 79, 126, 199, 315, 500, 794, 1265, 2009, 3202, 5090, 8108, 12898, 20533, 32667, 51990, 82721, 131631, 209446, 333263, 530282, 843764, 1342587, 2136280, 3399227, 5408765, 8606368, 13694288, 21790171, 34672157

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,-1,0,0,-2,0,5,0,-2,0,0,-1,-1,2,1,-1).

Formula

G.f.: -1/(x^9 * f(x) *f(1/x)), where f(x) = -1 +x^2 -x^7 -x^8 +x^9.

Mathematica

f[x_]:= -1 +x^2 -x^7 -x^8 +x^9;
CoefficientList[Series[-1/(x^9*f[x]*f[1/x]), {x, 0, 50}], x]

Prog

(PARI) Vec(1/(1 -x -2*x^2 +x^3 +x^4 +2*x^7 -5*x^9 +2*x^11 +x^14 +x^15 -2*x^16 -x^17 +x^18) + O(x^40)) \\ Jinyuan Wang, Mar 10 2020
(Magma)
f:= func< x | -1 + x^2 - x^7 - x^8 + x^9 >;
R<x>:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( -1/(x^9*f(x)*f(1/x)) )); // G. C. Greubel, Oct 21 2022
(SageMath)
def f(x): return -1 +x^2 -x^7 -x^8 +x^9
def A147622_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( -1/(x^9*f(x)*f(1/x)) ).list()
A147622_list(50) # G. C. Greubel, Oct 21 2022

Crossrefs

Sequence in context: A349050 A025034 A145722 * A173534 A074331 A052952

Adjacent sequences: A147619 A147620 A147621 * A147623 A147624 A147625

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 08 2008

Extensions

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

Status

approved