A309514 Number of winning Tak paths on an n X n board.

1, 4, 14, 56, 302

Offset

1,2

Comments

A "winning path" on any given Tak board is defined to be any path that connects one side of the grid to the opposite side, consistent with a path as defined by the rules of the game (see link), and which does not include within it a more direct winning path (a "shortcut").

The given terms (1, 4, 14, 56, 302) were generated by a combination of brute-force enumeration and generation by computer program (subsequently verified against an enumerated list).

Conjectured terms above n=5, generated by computer program, are 2012, 22574, 534312, 24816752, and 1908479044.

Links

Table of n, a(n) for n=1..5.

James Ernest et al., Rules of Tak

Crossrefs

Sequence in context: A346816 A006212 A126701 * A151884 A002735 A026652

Adjacent sequences: A309511 A309512 A309513 * A309515 A309516 A309517

Keyword

nonn,more

Author

Jakob Gowell, Aug 03 2019

Status

approved