A163436 - OEIS

%I #9 Sep 08 2022 08:45:46

%S 1,2,22,425,11550,403252,17164532,860938920,49684113582,3240906864140,

%T 235707022877304,18906047682170948,1657638292334575486,

%U 157698852357527675040,16177213677228994535040,1779883643542856425993296,209064002262265290212455374

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

%H G. C. Greubel, <a href="/A163436/b163436.txt">Table of n, a(n) for n = 1..335</a>

%F 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.

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

%t 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 *)

%o (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

%Y Cf. A162676, A163437

%K nonn

%O 1,2

%A _David Bevan_, Jul 28 2009