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%I #29 Oct 23 2022 23:32:58
%S 1,1,1,3,4,10,19,51,112,300,746,2042,5450,15197,42192,119561,339594
%N Number of digital images in Z^2 with 4-adjacency on n points up to isomorphism.
%C Also the number of polyominoes on n points, up to isomorphism of the adjacency graph.
%C Also the number of "grid graphs" (finite induced subgraphs of the integer lattice using only horizontal and vertical edges) on n vertices.
%H P. Christopher Staecker, <a href="http://arxiv.org/abs/1502.06236">Some enumerations of binary digital images</a>, arXiv 1502.06236 [math.CO], 2015.
%H Baoming Tang, Ehsan Khatami and Marcos Rigol, <a href="https://doi.org/10.1016/j.cpc.2012.10.008">A short introduction to numerical linked-cluster expansions</a>, Computer Physics Communications, 184 (2013), 557-564; arXiv:<a href="https://arxiv.org/abs/1207.3366">1207.3366</a> [cond-mat.stat-mech], 2012.
%e 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.
%Y Cf. A000105, A181528, A255540.
%K nonn,more,hard
%O 1,4
%A _P. Christopher Staecker_, Feb 24 2015
%E a(13)-a(16) from _Giovanni Resta_, Apr 10 2020
%E a(17) from Tang et al. added by _Andrey Zabolotskiy_, Oct 23 2022
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