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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 Table of n, a(n) for n=0..49. 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 Molien series 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 Adjacent sequences: A051527 A051528 A051529 * A051531 A051532 A051533 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane EXTENSIONS More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 15 2001 STATUS approved

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Last modified December 2 20:14 EST 2023. Contains 367526 sequences. (Running on oeis4.)