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%I #11 Sep 11 2020 15:45:37
%S 108,640,3500,18144,90552,439296,2084940,9724000,44710952,203164416,
%T 914004728,4077035200,18052470000,79420170240,347424465420,
%U 1512176830560,6552247686600,28276211040000,121580638419240,521033622457920
%N Number of (n+2)X(n+2) binary arrays avoiding patterns 001 and 101 in rows and columns
%C Diagonal of A202202
%H R. H. Hardin, <a href="/A202194/b202194.txt">Table of n, a(n) for n = 1..21</a>
%F Empirical: (n+1)*a(n) -2*(3n+4)*a(n-1) +4*(3n-2)*a(n-2) +8*(3-2n)*a(n-3)=0. - R. J. Mathar, Dec 14 2011
%F Conjecture: a(n) = 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!). - _Michael Somos_, Sep 11 2020
%e Some solutions for n=3
%e ..0..1..1..0..0....1..1..0..0..0....0..1..1..1..1....0..1..1..1..0
%e ..1..1..1..1..1....0..1..1..1..0....1..1..1..1..1....1..1..1..1..1
%e ..0..1..1..1..1....0..1..1..0..0....1..1..1..1..1....0..1..1..1..0
%e ..0..1..0..0..0....0..1..1..0..0....1..1..1..0..0....0..1..0..0..0
%e ..0..1..0..0..0....0..1..0..0..0....1..1..0..0..0....0..0..0..0..0
%o (PARI) {a(n) = if(n<1, 0, 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!))}; /* _Michael Somos_, Sep 11 2020 */
%K nonn
%O 1,1
%A _R. H. Hardin_ Dec 14 2011
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