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A296260
Number of preference profiles with 4 alternatives and n agents (IANC model).
1
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
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
KEYWORD
nonn
AUTHOR
Alexander Karpov, Dec 15 2017
EXTENSIONS
More terms from Michael De Vlieger, Dec 18 2017
STATUS
approved