A147607 Expansion of g.f.: 1/((1 - 2*x^2 + x^4 + 2*x^6 - x^8)*(1 - 2*x^2 - x^4 + 2*x^6 - x^8)).

1, 0, 4, 0, 12, 0, 28, 0, 59, 0, 116, 0, 228, 0, 460, 0, 968, 0, 2092, 0, 4564, 0, 9908, 0, 21309, 0, 45444, 0, 96484, 0, 204700, 0, 434999, 0, 926440, 0, 1976344, 0, 4218936, 0, 9005328, 0, 19212728, 0, 40970200, 0, 87341032, 0, 186180665, 0, 396899620

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 (0,4,0,-4,0,-4,0,11,0,-4,0,-4,0,4,0,-1).

Crossrefs

Cf. A122584, A147617.

Programs

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-2*x^2+x^4 +2*x^6-x^8)*(1-2*x^2-x^4+2*x^6-x^8)) )); // G. C. Greubel, Oct 24 2022

Mathematica

CoefficientList[Series[1/(1-4 x^2+4 x^4+4 x^6-11 x^8+4 x^10+4 x^12-4 x^14+x^16),{x,0,60}],x] (* or *) LinearRecurrence[ {0,4,0,-4,0,-4,0,11,0,-4,0,-4,0,4,0,-1},{1,0,4,0,12,0,28,0,59,0,116,0,228,0,460,0},60] (* Harvey P. Dale, Apr 03 2013 *)

SageMath

def A147607_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-2*x^2+x^4+2*x^6-x^8)*(1-2*x^2-x^4+2*x^6-x^8)) ).list()
A147607_list(60) # G. C. Greubel, Oct 24 2022

Formula

G.f.: 1/(1 - 4*x^2 + 4*x^4 + 4*x^6 - 11*x^8 + 4*x^10 + 4*x^12 - 4*x^14 + x^16).

a(n) = 4*a(n-2) - 4*a(n-4) - 4*a(n-6) + 11*a(n-8) - 4*a(n-10) - 4*a(n-12) + 4*a(n-14) - a(n-16) with a(0)=1, a(1)=0, a(2)=4, a(3)=0, a(4)=12, a(5)=0, a(6)=28, a(7)=0, a(8)=59, a(9)=0, a(10)=116, a(11)=0, a(12)=228, a(13)=0, a(14)=460, a(15)=0. - Harvey P. Dale, Apr 03 2013

G.f.: -1/(x^8*f(x)*f(1/x)), where f(x) = -1 + 2*x^2 - x^4 - 2*x^6 + x^8. - G. C. Greubel, Oct 24 2022

Extensions

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