A162676 Number of different fixed (possibly) disconnected n-ominoes bounded (not necessarily tightly) by an n*n square.

1, 4, 48, 956, 26490, 937342, 40291608, 2036155284, 118202408622, 7747410899954, 565695467415936, 45525704815717568, 4002930269944724664, 381750656962687053108, 39244733577786624617904, 4325973539461955182836900, 508971415418900757219557142

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

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

Example

a(2)=4: the two rotations of the (connected) domino and the two rotations of the disconnected domino consisting of two squares connected at a vertex.

Mathematica

Table[Binomial[n^2, n]-2*Binomial[(n-1)n, n]+Binomial[(n-1)^2, n], {n, 20}] (* Harvey P. Dale, Oct 01 2013 *)

Prog

(PARI) a(n) = binomial(n^2, n) - 2*binomial((n-1)*n, n) + binomial((n-1)^2, n); \\ Michel Marcus, Aug 30 2013

Crossrefs

Cf. A162673, A162674, A162675, A162677.

Sequence in context: A322296 A360484 A192260 * A141119 A052714 A144828

Adjacent sequences: A162673 A162674 A162675 * A162677 A162678 A162679

Keyword

nonn

Author

David Bevan, Jul 27 2009

Status

approved