A356049 Symmetric array read by antidiagonals: T(n,k) is the number of legal positions in Go on an n X k board.

1, 5, 5, 15, 57, 15, 41, 489, 489, 41, 113, 4125, 12675, 4125, 113, 313, 35117, 321689, 321689, 35117, 313, 867, 299681, 8180343, 24318165, 8180343, 299681, 867, 2401, 2557605, 208144601, 1840058693, 1840058693, 208144601, 2557605, 2401

Offset: 1

Author

Douglas Boffey, Jul 24 2022

Keywords

• nonn
• tabl

Comments

A Go position is a grid containing white and black stones with the condition that every orthogonally connected group of stones of a single color has liberties, i.e., is orthogonally adjacent to an empty cell.

Examples

			Array begins:
   1,   5,  15,  41, ...
   5,  57, 489, ...
  15, 489, ...
  41, ...
  ...
T(3,1) = 15 from
  ... ..w ..b .w. .ww  .b. .bb w.. w.w w.b  ww. b.. b.w b.b bb.
		

Links

• Douglas Boffey, Table of n, a(n) for n = 1..528
• J. Tromp, Number of Legal Go Positions

Crossrefs

Columns (or rows) give: A102620, A266278.

Main diagonal gives A094777.

This as triangle gives A356134.