OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Index entries for linear recurrences with constant coefficients, signature (5,-6,-10,29,-9,-36,36,9,-29,10,6,-5,1).
FORMULA
G.f.: (1 +2*x^2 +4*x^3 +x^4)/((1-x)^4*(1-x^2)^5).
G.f.: (1 -x +3*x^2 +x^3)/( (1+x)^4*(1-x)^9 ). - R. J. Mathar, Dec 18 2014
a(n) = ((315*(857+167*(-1)^n) + 60*(8347+581*(-1)^n)*n + (384718+6930*(-1)^n)*n^2 + 84*(2027+5*(-1)^n)*n^3 + 48888*n^4 + 9240*n^5 + 1092*n^6 + 72*n^7 + 2*n^8)) / 322560. - Colin Barker, Jan 16 2017
MAPLE
seq(coeff(series((1-x+3*x^2+x^3)/((1+x)^4*(1-x)^9), x, n+1), x, n), n = 0..40); # G. C. Greubel, Feb 02 2020
MATHEMATICA
LinearRecurrence[{5, -6, -10, 29, -9, -36, 36, 9, -29, 10, 6, -5, 1}, {1, 4, 17, 52, 147, 360, 819, 1712, 3382, 6312, 11286, 19368, 32154}, 35] (* Ray Chandler, Jul 15 2015 *)
PROG
(PARI) Vec((1 -x +3*x^2 +x^3)/((1-x)^9*(1+x)^4) + O(x^40)) \\ Colin Barker, Jan 16 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x+3*x^2+x^3)/((1+x)^4*(1-x)^9) )); // G. C. Greubel, Feb 02 2020
(Sage)
def A092091_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-x+3*x^2+x^3)/((1+x)^4*(1-x)^9) ).list()
A092091_list(40) # G. C. Greubel, Feb 02 2020
(GAP) List([0..40], n-> ((315*(857 +167*(-1)^n) +60*(8347 +581*(-1)^n)*n + (384718 +6930*(-1)^n)*n^2 +84*(2027 +5*(-1)^n)*n^3 +48888*n^4 +9240*n^5 +1092*n^6 +72*n^7 +2*n^8))/322560 ); # G. C. Greubel, Feb 02 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 01 2004
STATUS
approved