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Number of tilings of an n X n square using dominoes, monominoes and 2 X 2 tiles.
3

%I #13 May 08 2022 12:08:05

%S 1,1,8,163,15623,5684228,8459468955,50280716999785,

%T 1202536689448371122,115462301811597894998929,

%U 44537596159273736617786474211,69003082378039459280864860681919942,429429579883061866326542598342441907826951,10734684843612889640707750537898705644071715970757

%N Number of tilings of an n X n square using dominoes, monominoes and 2 X 2 tiles.

%H Alois P. Heinz, <a href="/A353777/b353777.txt">Table of n, a(n) for n = 0..17</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polyomino">Polyomino</a>

%F a(n) = A352589(n,n).

%e a(2) = 8:

%e .___. .___. .___. .___. .___. .___. .___. .___.

%e | | |_|_| |___| | | | |_|_| |___| |_| | | |_|

%e |___| |_|_| |___| |_|_| |___| |_|_| |_|_| |_|_| .

%Y Main diagonal of A352589.

%Y Cf. A004003, A028420, A063443, A219874, A219952, A219994, A220061, A220778, A233807, A270071.

%K nonn

%O 0,3

%A _Alois P. Heinz_, May 07 2022