A162676 - OEIS

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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

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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