A385053 Number of non-isomorphic simple games with n players and one minimal winning vector.

1, 3, 7, 15, 29, 55, 99, 176, 305, 522, 877, 1461, 2399, 3905, 6291, 10055, 15929, 25063, 39139, 60742, 93665, 143619, 218967, 332157, 501303, 753079, 1126155, 1676908, 2486641, 3673000, 5404711, 7924206, 11577465, 16858381, 24468317, 35402812, 51068703

Offset: 1

Author

Dani Samaniego Vidal, Jun 16 2025

Keywords

• nonn

Comments

a(n) is also the number of non-isomorphic monotonic boolean functions with one minimal model.

Links

• Sascha Kurz and Dani Samaniego, Simple games with minimum, arXiv:2501.18966 [math.CO], 2025.

Crossrefs

Second differences appear to be A052847.

Programs

Mathematica

sgnvnn[0,0] = 1; sgnvnn[_,0] = 0;
sgnvnn[n_,t_] := sgnvnn[n,t] = (1/t) Sum[If[Mod[k,l]==0, (k/l-1)sgnvnn[n-k,t-l], 0], {l,t},{k,n}];
sg[n_,1] := sgnvnn[n,1] + 1;
sg[n_,2] := sgnvnn[n,2] + 2 Sum[sgnvnn[n-i,1],{i,n-2}] + n - 1;
sg[n_,t_] := sgnvnn[n,t] + 2 Sum[sgnvnn[n-i,t-1],{i,n-2}] + Sum[(i-1) sgnvnn[n-i,t-2],{i,2,n-2}];
a[n_] := Sum[sg[n,t], {t,Quotient[n,2]+1}];
Table[a[n], {n,50}] (* Andrei Zabolotskii, Jul 24 2025 *)

Extensions

Edited and extended by Andrei Zabolotskii, Jul 24 2025