This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A037240 Molien series for 3-D group X1. 3
 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. 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: A098112 A237435 A280721 * A182095 A177432 A269740 Adjacent sequences:  A037237 A037238 A037239 * A037241 A037242 A037243 KEYWORD nonn,changed AUTHOR EXTENSIONS Terms a(35) and beyond from Alexander Karpov, Oct 29 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.