A163435 -id:A163435 - cp's OEIS frontend

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

David Bevan, Jul 28 2009

nonn

			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.

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

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

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 *)

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).

A163434 Number of different fixed (possibly) disconnected tetrominoes bounded tightly by an n X n square.

Original entry on oeis.org

0, 1, 70, 425, 1426, 3577, 7526, 14065, 24130, 38801, 59302, 87001, 123410, 170185, 229126, 302177, 391426, 499105, 627590, 779401, 957202, 1163801, 1402150, 1675345, 1986626, 2339377, 2737126, 3183545, 3682450, 4237801, 4853702

Offset: 1

David Bevan, Jul 28 2009

			a(2)=1: the (connected) square tetromino.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A162674, A163433, A163435, A163437.

Join[{0}, Table[(2 n^2 - 4 n + 1)*(3 n^2 - 6 n + 1), {n, 2, 50}]] (* or *) Join[{0}, LinearRecurrence[{5,-10,10,-5,1}, {1, 70, 425, 1426, 3577}, 50]] (* G. C. Greubel, Dec 23 2016 *)

concat([0], Vec(x^2*(1+65*x+85*x^2-9*x^3+2*x^4)/(1-x)^5 + O(x^50))) \\ G. C. Greubel, Dec 23 2016

a(n) = (2n^2 -4n +1)*(3n^2 -6n +1), n>1.
G.f.: x^2*(1+65*x+85*x^2-9*x^3+2*x^4)/(1-x)^5. - Colin Barker, Apr 25 2012
E.g.f.: (6*x^4 + 12*x^3 - x^2 + x + 1)*exp(x) - 2 x - 1. - G. C. Greubel, Dec 23 2016

cp's OEIS Frontend

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

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