A163436 Number of different fixed (possibly) disconnected n-ominoes bounded tightly by an n*n square.

1, 2, 22, 425, 11550, 403252, 17164532, 860938920, 49684113582, 3240906864140, 235707022877304, 18906047682170948, 1657638292334575486, 157698852357527675040, 16177213677228994535040, 1779883643542856425993296, 209064002262265290212455374

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..335

Formula

a(n)=binomial(n^2,n)-4*binomial((n-1)*n,n)+4*binomial((n-1)^2,n)+2*binomial((n-2)*n,n)-4*binomial((n-2)*(n-1),n)+binomial((n-2)^2,n), n>1.

Example

a(2)=2: the two rotations of the strictly disconnected domino consisting of two squares connected at a vertex

Mathematica

Join[{1}, Table[Binomial[n^2, n] - 4*Binomial[(n - 1)*n, n] + 4*Binomial[(n - 1)^2, n] + 2*Binomial[(n - 2)*n, n] - 4*Binomial[(n - 2)*(n - 1), n] + Binomial[(n - 2)^2, n], {n, 2, 50}]] (* G. C. Greubel, Dec 23 2016 *)

Prog

(Magma) [1] cat [Binomial(n^2, n)-4*Binomial((n-1)*n, n)+ 4*Binomial((n-1)^2, n)+2*Binomial((n-2)*n, n)-4*Binomial((n- 2)*(n-1), n)+Binomial((n-2)^2, n): n in [2..20]]; // Vincenzo Librandi, Dec 23 2016

Crossrefs

Cf. A162676, A163437

Sequence in context: A201511 A264839 A241347 * A328158 A266522 A360304

Adjacent sequences: A163433 A163434 A163435 * A163437 A163438 A163439

Keyword

nonn

Author

David Bevan, Jul 28 2009

Status

approved