A332714 The number of placements of zero or more dominoes on the n X n grid where the number of vertical dominoes differs from the number of horizontal dominoes by at most 1.

1, 5, 75, 4632, 1076492, 963182263, 3317770165381, 43809083383524391, 2209112327971366587064, 424273291301040427702718109, 309707064465485300360403957730000, 857932019835933358500355409793382735115, 9007779604382069542348587670082074125962102375

Offset

1,2

Comments

The number of play positions of n X n Domineering. 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

Table of n, a(n) for n=1..13.

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.

Prog

(Sage) # See Bjorn Huntemann, Svenja Huntemann, Neil A. McKay link.

Crossrefs

Cf. A028420 (the number of placements of dominoes on an n X n grid).

Cf. A330658, A332865.

Sequence in context: A132855 A238560 A303125 * A258784 A051481 A277296

Adjacent sequences: A332711 A332712 A332713 * A332715 A332716 A332717

Keyword

nonn

Author

Neil A. McKay, Feb 20 2020

Extensions

a(11)-a(13) from Andrew Howroyd, Feb 20 2020

Status

approved