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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.

Index entries for Molien series

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

N. J. A. Sloane

EXTENSIONS

Terms a(35) and beyond from Alexander Karpov, Oct 29 2017

STATUS

approved

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Last modified December 11 12:00 EST 2017. Contains 295876 sequences.