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

1, 7, 322, 51472, 29671936, 64588152832, 545697103347712, 18161310923858378752, 2399054119350722118025216, 1262710910458264839283982467072, 2653270028014955753823799266500411392

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..55

Formula

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).

Example

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.

Mathematica

Table[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), {n, 1, 25}] (* G. C. Greubel, Dec 23 2016 *)

Crossrefs

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

Sequence in context: A244851 A082160 A220278 * A109059 A002000 A374418

Adjacent sequences: A163434 A163435 A163436 * A163438 A163439 A163440

Keyword

nonn

Author

David Bevan, Jul 28 2009

Status

approved