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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 (list; graph; refs; listen; history; text; internal format)
 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: A226117 A221173 A330138 * A240670 A048040 A051033 Adjacent sequences:  A051527 A051528 A051529 * A051531 A051532 A051533 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 15 2001 STATUS approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)