login
a(n) is the minimal number of legal positions in Go played on connected graphs with n nodes.
0

%I #10 Sep 13 2020 16:45:47

%S 1,5,15,41,107,273,707,1817,4617,11867,30425,76857,197603,505871,

%T 1275465,3276563,8406527,21165273,54338627,139513379,351447657,

%U 901789811,2304725075,5840498937,14978318243,38107010435,97141424265,248995117523,630641012147

%N a(n) is the minimal number of legal positions in Go played on connected graphs with n nodes.

%C Consider a Go game played on general graphs instead of grids. The position that each group has at least one liberty is called a legal position. 2^(n+1)-3 and 3^n-2^n are respectively the trivial lower bound and upper bound of this sequence. The Mathematics of Go interest group computed this sequence up to n=481.

%Y Cf. A094777, A102620, A266278, A268113, A327821.

%K nonn

%O 1,2

%A _Zhujun Zhang_, Aug 19 2020