A255539 Number of digital images in Z^2 with 4-adjacency on n points up to isomorphism.

1, 1, 1, 3, 4, 10, 19, 51, 112, 300, 746, 2042, 5450, 15197, 42192, 119561, 339594

Offset

1,4

Comments

Also the number of polyominoes on n points, up to isomorphism of the adjacency graph.

Also the number of "grid graphs" (finite induced subgraphs of the integer lattice using only horizontal and vertical edges) on n vertices.

Links

Table of n, a(n) for n=1..17.

P. Christopher Staecker, Some enumerations of binary digital images, arXiv 1502.06236 [math.CO], 2015.

Baoming Tang, Ehsan Khatami and Marcos Rigol, A short introduction to numerical linked-cluster expansions, Computer Physics Communications, 184 (2013), 557-564; arXiv:1207.3366 [cond-mat.stat-mech], 2012.

Example

a(4) = 3: (1) the square tetromino has the 4-cycle as its "adjacency graph"; (2) the T-tetromino corresponds to the claw graph; (3) the straight, skew, and L-tetromino all correspond to the 4-path.

Crossrefs

Cf. A000105, A181528, A255540.

Sequence in context: A306334 A036649 A345322 * A326832 A357812 A321197

Adjacent sequences: A255536 A255537 A255538 * A255540 A255541 A255542

Keyword

nonn,more,hard

Author

P. Christopher Staecker, Feb 24 2015

Extensions

a(13)-a(16) from Giovanni Resta, Apr 10 2020

a(17) from Tang et al. added by Andrey Zabolotskiy, Oct 23 2022

Status

approved