A332865 Number of placements of zero or more dominoes on the n X n grid where no two empty squares are horizontally adjacent.

1, 4, 48, 1427, 140555, 40008789, 33656587715, 84588476099284, 626461671945179295, 13776144517953719025396, 897220763259635483826935324, 173109540246969825014223808529273, 98978509126162805673620043358494745638, 167661422725328648892707605323564506782035252

Offset: 1

Author

Neil A. McKay, Feb 27 2020

Keywords

• nonn

Comments

The number of positions of n X n Domineering where horizontal (Right) has no moves, also called Right ends. Domineering is a game in which players take turns placing dominoes on a grid, one player placing vertically and the other horizontally until the player to place cannot place a domino.

Links

• Bjorn Huntemann, Svenja Huntemann, and Neil A. McKay SageMath code for Counting Domineering Positions
• Svenja Huntemann and Neil A. McKay, Counting Domineering Positions, arXiv:1909.12419 [math.CO], 2019.

Crossrefs

Main diagonal of A332862.

Cf. A287595 (the number of placements of dominoes on an n X n grid where no two empty squares are horizontally or vertically adjacent).

Cf. A332714.

Programs

Sage

# See Bjorn Huntemann, Svenja Huntemann, Neil A. McKay link.

Extensions

a(9)-a(14) from Andrew Howroyd, Feb 28 2020