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 A037240 Molien series for 3-D group X1. 5
 1, 1, 5, 10, 24, 42, 83, 132, 222, 335, 511, 728, 1047, 1428, 1956, 2586, 3414, 4389, 5638, 7084, 8888, 10966, 13494, 16380, 19841, 23751, 28371, 33566, 39616, 46376, 54177, 62832, 72726, 83661, 96045, 109668, 124999, 141778, 160538, 181006, 203742, 228459, 255788, 285384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also multidigraphs with 3 nodes and n arcs. - Vladeta Jovovic, Dec 27 1999 Also preference profiles with 3 alternatives and n agents (IANC model). - Alexander Karpov, Nov 23 2017 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Ö. Egecioglu, Uniform generation of anonymous and neutral preference profiles for social choice rules, Technical Report, UCSB, 2005. Ö. Egecioglu, Uniform generation of anonymous and neutral preference profiles for social choice rules, Monte Carlo Methods and Applications, 15(3), Jan 2009, 241-255. Marko V. Jaric and Joseph L. Birman, Calculation of the Molien generating function for invariants of space groups, J. Math. Phys. 18 (1977), 1459-1465; 2085. Alexander V. Karpov, An Informational Basis for Voting Rules, NRU Higher School of Economics. Series WP BRP "Economics/EC". 2018. No. 188. FORMULA G.f.: (1 + x^2 + 3*x^3 + 5*x^4 + x^5 + x^6)/(1 - x)/(1 - x^2)^3/(1 - x^3)^2. From Alexander Karpov, Nov 18 2017: (Start) if n ==  0  mod 6, a(n) = C(n+5,5)/6 + (n+4)*(n+2)/16 + (n+3)/9; if n ==  3  mod 6, a(n) = C(n+5,5)/6 + (n+3)/9; if n == 2,4 mod 6, a(n) = C(n+5,5)/6 + (n+4)*(n+2)/16; if n == 1,5 mod 6, a(n) = C(n+5,5)/6. (End) MAPLE S:= series((1+x^2+3*x^3+5*x^4+x^5+ x^6)/(1 - x)/(1 - x^2)^3/(1 - x^3)^2, x, 101): seq(coeff(S, x, n), n=0..100); # Robert Israel, Nov 22 2017 MATHEMATICA CoefficientList[Series[(1 + x^2 + 3 x^3 + 5 x^4 + x^5 + x^6)/(1 - x)/(1 - x^2)^3/(1 - x^3)^2, {x, 0, 43}], x] (* Michael De Vlieger, Nov 01 2017 *) PROG (PARI) Vec((1+x^2+3*x^3+5*x^4+x^5+x^6)/(1-x)/(1-x^2)^3/(1-x^3)^2 + O(x^50)) \\ Michel Marcus, Oct 31 2017 CROSSREFS Sequence in context: A237435 A280721 A300552 * A182095 A177432 A269740 Adjacent sequences:  A037237 A037238 A037239 * A037241 A037242 A037243 KEYWORD nonn AUTHOR EXTENSIONS Terms a(35) and beyond from Alexander Karpov, Oct 29 2017 STATUS approved

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Last modified July 18 21:23 EDT 2018. Contains 312765 sequences. (Running on oeis4.)