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%I #35 May 01 2020 13:17:00
%S 1,4,22,113,571,2816,13616,64678,302574,1397318,6382660,28882214,
%T 129640058,577812724,2559491834,11276000877,49437494408,215815377168
%N Number of n-ominoes in n X n grid (i.e., rookwise connected sets of n cells in a square array with n rows and n columns).
%C Higher corrected values are supported by exhibiting a(n) distinct n-ominoes in the n-square for n=10 and n=11 (see LINKS below). - _James Stein_, Dec 11 2017
%C a(n) is the number of connected induced subgraphs with n vertices in the n X n grid graph. - _Andrew Howroyd_, Apr 27 2020
%D This sequence will some day be mentioned in an exercise in section 7.2.2 of The Art of Computer Programming.
%H James Stein, <a href="https://goo.gl/RzpsaQ">1397318 gzipped 10-ominoes</a>
%H James Stein, <a href="https://goo.gl/NPbWYi">6382660 gzipped 11-ominoes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%e The 22 arrangements for n=3 include three horizontal rows, three vertical rows, and four ways to place each rotation of the L-tromino.
%Y Cf. A001168, A059525, A162676.
%K nonn,more
%O 1,2
%A _Don Knuth_, Apr 29 2016
%E a(10)-a(12) corrected, and a(13)-a(14) added by _James Stein_, Dec 11 2017
%E a(15)-a(16) from _Andrew Howroyd_, Apr 27 2020
%E a(17)-a(18) from _Giovanni Resta_, May 01 2020
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