OFFSET
0,5
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II Codes, Even Unimodular Lattices and Invariant Rings, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,1,-1,-1,1,-2,2,0,0,1,-1).
FORMULA
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=4, a(5)=2, a(6)=3, a(7)=2, a(8)=11, a(9)=7, a(10)=11, a(11)=9, a(12)=25, a(13)=18, a(14)=27, a(n)=a(n-1)+ 2*a(n-4)- 2*a(n-5)+ a(n-6)- a(n-7)-a(n-8)+a(n-9)-2*a(n-10)+ 2*a(n-11)+ a(n-14)-a(n-15). - Harvey P. Dale, Mar 04 2013
a(n) ~ 1/144*n^3. - Ralf Stephan, May 17 2014
G.f.: (x^12-x^9+2*x^8+2*x^4-x+1) / ((x-1)^4*(x+1)^3*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)). - Colin Barker, Apr 02 2015
MAPLE
(1+x)*(1+x^2)*(1-x+2*x^4+2*x^8-x^9+x^12)/((1-x^4)^3*(1-x^6));
MATHEMATICA
CoefficientList[Series[(1+x)*(1+x^2)*(1-x+2*x^4+2*x^8-x^9+x^12)/((1-x^4)^3*(1-x^6)), {x, 0, 60}], x] (* or *) LinearRecurrence[ {1, 0, 0, 2, -2, 1, -1, -1, 1, -2, 2, 0, 0, 1, -1}, {1, 0, 0, 0, 4, 2, 3, 2, 11, 7, 11, 9, 25, 18, 27}, 60] (* Harvey P. Dale, Mar 04 2013 *)
PROG
(PARI) Vec((x^12-x^9+2*x^8+2*x^4-x+1)/((x-1)^4*(x+1)^3*(x^2-x+1)*(x^2+1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 02 2015
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved