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A057051 Number of polyominoes of 2n-1 cells that span an n X n square.

%I A057051 #15 Mar 21 2024 21:00:34
%S A057051 1,1,6,18,73,255,950,3473,13006,48840,185353,706404,2706608,10404625,
%T A057051 40126430,155133811,601119492,2333671638,9075290555,35345525798,
%U A057051 137847145330,538258922839,2104101413400,8233434921693,32247613423563,126410623214720,495918571702575
%N A057051 Number of polyominoes of 2n-1 cells that span an n X n square.
%H A057051 D. E. Knuth, <a href="http://www.jstor.org/stable/3647949">Animals in a cage, Problem 10875</a>, Amer. Math. Monthly, 110 (March 2003), 243-245.
%H A057051 R. J. Mathar, <a href="http://www.vixra.org/abs/1905.0474">Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)"</a> viXra:1905.0474 (2019)
%H A057051 R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
%F A057051 See Maple code.
%p A057051 A057051 := proc(n) if n mod 2 = 0 then binomial(2*n-2,n-1)+2^(n-2)-(3*n^2-2*n+8)/8; else binomial(2*n-2,n-1)+2^(n-2)-(3*n^2-4*n+9)/8+(1/2)*binomial(n-1,(n-1)/2); end if; end proc;
%t A057051 f[n_] := If[EvenQ[n], Binomial[2n-2, n-1] + 2^(n-2) - (3n^2-2n+8)/8, Binomial[2n-2, n-1] + 2^(n-2) - (3n^2-4n+9)/8 + (1/2) Binomial[n-1, (n-1)/2]]; Table[f[n], {n, 1, 27}] (* _Jean-François Alcover_, Mar 18 2017, translated from Maple *)
%K A057051 nonn
%O A057051 1,3
%A A057051 _N. J. A. Sloane_, Mar 08 2003