A337207 a(n) is the minimal number of legal positions in Go played on connected graphs with n nodes.

1, 5, 15, 41, 107, 273, 707, 1817, 4617, 11867, 30425, 76857, 197603, 505871, 1275465, 3276563, 8406527, 21165273, 54338627, 139513379, 351447657, 901789811, 2304725075, 5840498937, 14978318243, 38107010435, 97141424265, 248995117523, 630641012147

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..29.

Crossrefs

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

Sequence in context: A038066 A306159 A113861 * A080870 A288414 A102620

Adjacent sequences: A337204 A337205 A337206 * A337208 A337209 A337210

Keyword

nonn

Author

Zhujun Zhang, Aug 19 2020

Status

approved