OFFSET
0,2
COMMENTS
The sequence seems based on the assumption that the game starts with an empty 19 X 19 board, which is not necessarily the case in an official Go tournament. After any of the 361 = 19^2 choices for the first move, the opponent has 360 = 19^2 - 1 choices for placing his stone, so the value a(2) = (360 + 1) * 361 takes into account the possibility of not placing a stone. A detailed account of the precise rules used here would be useful to make the definition of this sequence complete. - M. F. Hasler, Nov 22 2016
Only unterminated Go games of exactly n moves are counted. Players may pass their turn, but the final move must be a stone placement on the board. Furthermore, two consecutive passes terminate the game, so any game containing them is excluded. A stone placement is strictly prohibited if it is a suicide (leaving the stone with no liberties, without capturing opponent stones) or if it violates the Superko rule, defined as any stone placement that recreates a board position previously seen in the current game. - Jinyuan Wang, May 02 2026
LINKS
Daniel Forgues, Game of Go, OEIS wiki, Feb. 2016.
Sensei's Library, Rules of Go - introductory.
FORMULA
EXAMPLE
From Jinyuan Wang, May 02 2026: (Start)
Let P denote a pass, B denote a Black stone placement, and W denote a White stone placement. For n = 4, there are 5 valid move patterns:
PWPW: 361 * 360 = 129960
PWBW: 361 * 360 * 359 = 46655640
BPBW: 361 * 360 * 359 - 8 = 46655632 (Black can occupy the two adjacent intersections of an empty corner in 4 * 2 ways. In those 8 variations, the surrounded corner becomes a suicide point for White's final move.)
BWPW: 361 * 360 * 359 = 46655640
BWBW: 361 * 360 * 359 * 358 - 8 * 358 = 16702716256
Therefore, the number of Go games with exactly 4 moves is 129960 + 46655640 + 46655632 + 46655640 + 16702716256 = 16842813128. (End)
CROSSREFS
KEYWORD
nonn,nice,hard,more,fini
AUTHOR
EXTENSIONS
a(4) and a(5) corrected by Jinyuan Wang, May 02 2026
STATUS
approved