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 (0,4,0,-4,0,-4,0,11,0,-4,0,-4,0,4,0,-1).
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
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 *)
PROG
(Magma) R<x>:=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
(SageMath)
def A147607_list(prec):
P.<x> = 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
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Nov 08 2008
EXTENSIONS
Definition corrected by N. J. A. Sloane, Nov 09 2008
STATUS
approved