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

1,3

Links

Table of n, a(n) for n=1..27.

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.

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.

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 *)

Crossrefs

Cf. A037240 for 3 alternatives.

Sequence in context: A264723 A157099 A108649 * A139858 A139903 A362225

Adjacent sequences: A296257 A296258 A296259 * A296261 A296262 A296263

Keyword

nonn

Author

Alexander Karpov, Dec 15 2017

Extensions

More terms from Michael De Vlieger, Dec 18 2017

Status

approved