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 A051461 Molien series for group G_{1,3} of order 2304. 2
 1, 0, 1, 15, 37, 78, 229, 419, 721, 1341, 2152, 3214, 5083, 7324, 10167, 14485, 19637, 25772, 34575, 44663, 56511, 72419, 90552, 111188, 138093, 168064, 201909, 244403, 291549, 343794, 408225, 478659, 556325, 649809, 751696, 862642, 994583, 1136908, 1291355, 1471945 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Index entries for linear recurrences with constant coefficients, signature (1,1,1,-2,-2,3,-1,-1,-3,4,4,-3,-1,-1,3,-2,-2,1,1,1,-1). 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. FORMULA G.f.: (x^18 + 4*x^17 + 19*x^16 + 30*x^15 + 47*x^14 + 97*x^13 + 128*x^12 + 113*x^11 + 186*x^10 + 161*x^9 + 97*x^8 + 108*x^7 + 98*x^6 + 27*x^5 + 23*x^4 + 13*x^3 - x + 1)/((x - 1)^6*(x + 1)^3*(x^2 + x + 1)^4*(x^2 - x + 1)^2). a(n) ~ 2*n^5/135. - Stefano Spezia, Aug 21 2022 MATHEMATICA CoefficientList[Series[(x^18+4x^17+19x^16+30x^15+47x^14+97x^13+ 128x^12+ 113x^11+ 186x^10+161x^9+97x^8+108x^7+ 98x^6+27x^5+23x^4+13x^3-x+1)/ ((x-1)^6(x+1)^3(x^2+x+1)^4(x^2-x+1)^2), {x, 0, 40}], x] (* Harvey P. Dale, Jan 28 2015 *) CROSSREFS Cf. A051462, A051463. Sequence in context: A082112 A059605 A147221 * A321383 A039605 A032654 Adjacent sequences: A051458 A051459 A051460 * A051462 A051463 A051464 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 6 11:47 EST 2023. Contains 360104 sequences. (Running on oeis4.)