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%I #20 Jul 18 2013 18:00:39
%S 16,28,78,260,932,3440,12878,48628,184764,705440,2704164,10400608,
%T 40116608,155117528,601080398,2333606228,9075135308,35345263808,
%U 137846528828,538257874448,2104098963728,8233430727608,32247603683108
%N Number of (n+1) X (n+1) 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
%C Diagonal of A206267.
%H R. H. Hardin and Vincenzo Librandi, <a href="/A206259/b206259.txt">Table of n, a(n) for n = 1..1000</a> (first 69 terms from R. H. Hardin).
%F Recurrence (for n>3): (n+1)*(3*n-2)*a(n) = (15*n^2-n-4)*a(n-1) - 2*(2*n-1)*(3*n+1)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F a(n) = 8+2*C(2*n+1,n), for n>1. - _Vaclav Kotesovec_, Oct 28 2012
%e Some solutions for n=4
%e ..1..1..0..0..0....0..1..0..1..0....1..1..1..1..0....1..1..0..0..0
%e ..1..0..0..0..0....1..0..1..0..1....0..0..0..0..0....1..0..0..0..0
%e ..0..0..0..0..0....0..1..0..1..0....0..0..0..0..0....1..0..0..0..0
%e ..0..0..0..0..0....1..0..1..0..1....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..0..0....0..1..0..1..0....0..0..0..0..0....0..0..0..0..0
%t Flatten[{16,Table[8+2*Binomial[2*n+1,n],{n,2,20}]}] (* _Vaclav Kotesovec_, Oct 28 2012 *)
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012
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