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%I #8 Nov 20 2018 16:32:26
%S 1296,5139,18537,62469,201741,634509,1962717,6007149,18260061,
%T 55258029,166730397,502104429,1510140381,4538075949,13629538077,
%U 40919235309,122818948701,368579332269,1105982969757,3318438855789,9956296461021
%N Number of (n+1) X (6+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H R. H. Hardin, <a href="/A250810/b250810.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(n) = (1904*3^n - 1869*2^n + 618)/2.
%F Empirical g.f.: 3*x*(432 - 879*x + 653*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Nov 20 2018
%e Some solutions for n=4:
%e ..2..2..2..2..2..2..1....2..2..2..2..2..2..0....2..2..1..1..1..0..0
%e ..1..1..1..1..1..1..1....0..0..0..0..0..0..0....0..0..0..0..0..0..0
%e ..0..0..0..0..1..1..1....2..2..2..2..2..2..2....0..1..1..1..1..1..1
%e ..1..1..1..1..2..2..2....1..1..1..1..1..1..1....0..1..1..1..1..2..2
%e ..0..0..0..1..2..2..2....1..1..2..2..2..2..2....0..1..1..1..1..2..2
%Y Column 6 of A250812.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014
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