A269417 Number of Go games on n X n board with no repeating position and suicide allowed.

1, 1, 386356909593

Offset

0,3

Comments

I only chose starting offset 0 because the number of 3 X 3 games is unknown (and over a thousand digits).

a(n) is also the number of simple paths in the Go game graph starting at the empty position.

a(n) is upper bounded by n^{2*3^{n^2}}, as shown in Theorem 7 from the linked paper.

Links

Table of n, a(n) for n=0..2.

J. Tromp and G. Farnebäck, Combinatorics of Go, Lecture Notes in Computer Science, 4630, 84-99, 2007.

Example

a(1) = 1 since the only legal Go game on a 1 X 1 board is Black pass, White pass.

Crossrefs

Cf. A094777.

Sequence in context: A172714 A080132 A080122 * A281963 A357687 A363799

Adjacent sequences: A269414 A269415 A269416 * A269418 A269419 A269420

Keyword

nonn,more,bref,hard

Author

John Tromp, Feb 25 2016

Status

approved