cp's OEIS Frontend

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

%I A385053 #23 Jul 25 2025 09:00:53
%S A385053 1,3,7,15,29,55,99,176,305,522,877,1461,2399,3905,6291,10055,15929,
%T A385053 25063,39139,60742,93665,143619,218967,332157,501303,753079,1126155,
%U A385053 1676908,2486641,3673000,5404711,7924206,11577465,16858381,24468317,35402812,51068703
%N A385053 Number of non-isomorphic simple games with n players and one minimal winning vector.
%C A385053 a(n) is also the number of non-isomorphic monotonic boolean functions with one minimal model.
%H A385053 Sascha Kurz and Dani Samaniego, <a href="https://arxiv.org/abs/2501.18966">Simple games with minimum</a>, arXiv:2501.18966 [math.CO], 2025.
%t A385053 sgnvnn[0,0] = 1; sgnvnn[_,0] = 0;
%t A385053 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}];
%t A385053 sg[n_,1] := sgnvnn[n,1] + 1;
%t A385053 sg[n_,2] := sgnvnn[n,2] + 2 Sum[sgnvnn[n-i,1],{i,n-2}] + n - 1;
%t A385053 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}];
%t A385053 a[n_] := Sum[sg[n,t], {t,Quotient[n,2]+1}];
%t A385053 Table[a[n], {n,50}] (* _Andrei Zabolotskii_, Jul 24 2025 *)
%Y A385053 Second differences appear to be A052847.
%K A385053 nonn
%O A385053 1,2
%A A385053 _Dani Samaniego Vidal_, Jun 16 2025
%E A385053 Edited and extended by _Andrei Zabolotskii_, Jul 24 2025