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%I #7 Nov 15 2018 14:03:47
%S 81,169,345,697,1401,2809,5625,11257,22521,45049,90105,180217,360441,
%T 720889,1441785,2883577,5767161,11534329,23068665,46137337,92274681,
%U 184549369,369098745,738197497,1476395001,2952790009,5905580025
%N Number of (n+1) X (7+1) 0..1 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="/A250655/b250655.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*49 + (5*2^(n-1)-1)*7 +2^(n+1).
%F Empirical g.f.: x*(81 - 74*x) / ((1 - x)*(1 - 2*x)). - _Colin Barker_, Nov 15 2018
%e Some solutions for n=4:
%e ..1..1..0..0..0..0..0..0....1..1..1..1..0..0..0..0....1..1..1..1..0..0..0..0
%e ..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
%e ..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....1..1..1..1..1..1..1..1
%e ..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....1..1..1..1..1..1..1..1
%e ..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....0..0..0..0..0..1..1..1
%Y Column 7 of A250656.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 26 2014
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