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A051530
Molien series for group H_{1,3} of order 1152.
0
1, 0, 1, 3, 4, 5, 15, 14, 24, 35, 44, 54, 81, 88, 115, 143, 168, 195, 247, 270, 322, 375, 424, 476, 561, 608, 693, 779, 860, 945, 1071, 1150, 1276, 1403, 1524, 1650, 1825, 1944, 2119, 2295, 2464, 2639, 2871, 3038, 3270, 3503, 3728, 3960, 4257, 4480
OFFSET
0,4
LINKS
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, 1, 0, -1, -1, 2, -1, -1, 0, 1, 1, -1).
FORMULA
G.f.: (x^9+x^8-x^7+5*x^6-x^5+x^4+2*x^3-x+1)/((x-1)^4*(x+1)^2*(x^2+x+1)^2*(x^2-x+1)).
a(0)=1, a(1)=0, a(2)=1, a(3)=3, a(4)=4, a(5)=5, a(6)=15, a(7)=14, a(8)=24, a(9)=35, a(10)=44, a(11)=54, a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-5)+ 2*a(n-6)-a(n-7)-a(n-8)+a(n-10)+a(n-11)-a(n-12). - Harvey P. Dale, Jun 15 2013
a(n) ~ 1/27 * n^3. - Ralf Stephan, May 17 2014
MATHEMATICA
CoefficientList[Series[(x^9+x^8-x^7+5x^6-x^5+x^4+2x^3-x+1)/((x-1)^4 (x+1)^2(x^2+x+1)^2(x^2-x+1)), {x, 0, 50}], x] (* or *) LinearRecurrence[ {1, 1, 0, -1, -1, 2, -1, -1, 0, 1, 1, -1}, {1, 0, 1, 3, 4, 5, 15, 14, 24, 35, 44, 54}, 50] (* Harvey P. Dale, Jun 15 2013 *)
CROSSREFS
Sequence in context: A221173 A346599 A330138 * A240670 A048040 A347391
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 15 2001
STATUS
approved