A296260 Number of preference profiles with 4 alternatives and n agents (IANC model).

1, 1, 17, 111, 762, 4095, 19941, 84825, 329214, 1168740, 3858348, 11920740, 34773590, 96282900, 254473884, 644637204, 1571330916, 3697182450, 8421423582, 18615637950, 40023753924, 83859017814, 171530071362, 343059613650, 671825586021, 1289904147324, 2430974136780

Offset: 1

Author

Alexander Karpov, Dec 15 2017

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A037240 for 3 alternatives.

Programs

Mathematica

Array[Binomial[# + 23, 23]/24 + Which[Divisible[#1, 12], 3 Binomial[#1/2 + 11, 11]/8 + Binomial[#1/3 + 7, 7]/3 + Binomial[#1/4 + 5, 5]/4, MemberQ[{1, 5, 7, 11}, #2], 0, MemberQ[{2, 10}, #2], 3 Binomial[#1/2 + 11, 11]/8, MemberQ[{3, 9}, #2], Binomial[#1/3 + 7, 7]/3, MemberQ[{4, 8}, #2], 3 Binomial[#1/2 + 11, 11]/8 + Binomial[#1/4 + 5, 5]/4, True, 3 Binomial[#1/2 + 11, 11]/8 + Binomial[#1/3 + 7, 7]/3 ] & @@ {#, Mod[#, 12]} &, 26] (* Michael De Vlieger, Dec 18 2017 *)

Formula

if n == 0 mod 12, a(n) = C(n+23,23)/24 + C(n/2+11,11)*3/8 + C(n/3+7,7)/3+C(n/4+5,5)/4;

if n == 1,5,7,11 mod 12, a(n) = C(n+23,23)/24;

if n == 2,10 mod 12, a(n) = C(n+23,23)/24 + C(n/2+11,11)*3/8;

if n == 3,9 mod 12, a(n) = C(n+23,23)/24 + C(n/3+7,7)/3;

if n == 4,8 mod 12, a(n) = C(n+23,23)/24 + C(n/2+11,11)*3/8 +C(n/4+5,5)/4;

if n == 6 mod 12, a(n) = C(n+23,23)/24 + C(n/2+11,11)*3/8 + C(n/3+7,7)/3.

Extensions

More terms from Michael De Vlieger, Dec 18 2017