A147606 Expansion of g.f.: 1/((1 - x - x^2 + x^4 - x^6)*(1 - x^2 + x^4 + x^5 - x^6)).

1, 1, 3, 4, 6, 8, 12, 15, 25, 35, 56, 84, 130, 192, 294, 432, 654, 972, 1466, 2192, 3308, 4953, 7463, 11185, 16820, 25224, 37906, 56868, 85445, 128239, 192643, 289196, 434364, 652124, 979372, 1470436, 2208192, 3315556, 4978892, 7475948, 11226252

Offset: 0

Author

Roger L. Bagula, Nov 08 2008

Keywords

• nonn
• easy

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,-3,0,5,0,-3,-1,2,1,-1).

Crossrefs

Cf. A109537, A147607, A147617.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x-x^2+x^4-x^6)*(1-x^2+x^4+x^5-x^6)) )); // G. C. Greubel, Oct 24 2022

Mathematica

f[x_]= -1+x+x^2-x^4+x^6;
CoefficientList[Series[-1/(x^6*f[x]*f[1/x]), {x, 0, 50}], x] (* G. C. Greubel, Oct 24 2022 *)

SageMath

def A147606_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x-x^2+x^4-x^6)*(1-x^2+x^4+x^5-x^6)) ).list()
A147606_list(50) # G. C. Greubel, Oct 24 2022

Formula

G.f.: 1/(1 - x - 2*x^2 + x^3 + 3*x^4 - 5*x^6 + 3*x^8 + x^9 - 2*x^10 - x^11 + x^12).

G.f.: -1/(x^6*f(x)*f(1/x)), where f(x) = -1 + x + x^2 - x^4 + x^6. - G. C. Greubel, Oct 24 2022

Extensions

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