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

1,2

Comments

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

Links

Table of n, a(n) for n=1..37.

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

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 *)

Crossrefs

Second differences appear to be A052847.

Sequence in context: A321309 A373090 A023608 * A218189 A132780 A018087

Adjacent sequences: A385050 A385051 A385052 * A385054 A385055 A385056

Keyword

nonn

Author

Dani Samaniego Vidal, Jun 16 2025

Extensions

Edited and extended by Andrei Zabolotskii, Jul 24 2025

Status

approved