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A163437 Number of different fixed (possibly) disconnected polyominoes (of any area) bounded tightly by an n X n square. 5

%I

%S 1,7,322,51472,29671936,64588152832,545697103347712,

%T 18161310923858378752,2399054119350722118025216,

%U 1262710910458264839283982467072,2653270028014955753823799266500411392

%N Number of different fixed (possibly) disconnected polyominoes (of any area) bounded tightly by an n X n square.

%H G. C. Greubel, <a href="/A163437/b163437.txt">Table of n, a(n) for n = 1..55</a>

%F a(n) = 2^(n^2) - 4*2^((n-1)*n) + 4*2^((n-1)^2) + 2*2^((n-2)*n) - 4*2^((n-2)*(n-1)) + 2^((n-2)^2).

%e a(2)=7: 2 rotations of the strictly disconnected domino consisting of two squares connected at a vertex, 4 rotations of the L tromino, and the square tetromino.

%t Table[2^(n^2) - 4*2^((n - 1)*n) + 4*2^((n - 1)^2) + 2*2^((n - 2)*n) -

%t 4*2^((n - 2)*(n - 1)) + 2^((n - 2)^2), {n, 1, 25}] (* _G. C. Greubel_, Dec 23 2016 *)

%Y Cf. A162677 (bound not necessarily tight), A163433 (fixed disconnected trominoes), A163434 (fixed disconnected tetrominoes), A163435 (fixed disconnected pentominoes), A163436 (fixed disconnected n-ominoes).

%K nonn

%O 1,2

%A _David Bevan_, Jul 28 2009

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Last modified July 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)