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A250660 Number of (6+1) X (n+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.

%I A250660 #7 Nov 15 2018 14:58:50
%S A250660 319,574,893,1276,1723,2234,2809,3448,4151,4918,5749,6644,7603,8626,
%T A250660 9713,10864,12079,13358,14701,16108,17579,19114,20713,22376,24103,
%U A250660 25894,27749,29668,31651,33698,35809,37984,40223,42526,44893,47324,49819,52378,55001
%N A250660 Number of (6+1) X (n+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 A250660 R. H. Hardin, <a href="/A250660/b250660.txt">Table of n, a(n) for n = 1..210</a>
%F A250660 Empirical: a(n) = 32*n^2 + 159*n + 128.
%F A250660 Conjectures from _Colin Barker_, Nov 15 2018: (Start)
%F A250660 G.f.: x*(319 - 383*x + 128*x^2) / (1 - x)^3.
%F A250660 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250660 (End)
%e A250660 Some solutions for n=4:
%e A250660 ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....1..1..0..0..0
%e A250660 ..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
%e A250660 ..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1
%e A250660 ..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
%e A250660 ..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
%e A250660 ..0..0..0..0..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..1
%e A250660 ..0..0..0..0..1....0..1..1..1..1....1..1..1..1..1....0..0..0..0..0
%Y A250660 Row 6 of A250656.
%K A250660 nonn
%O A250660 1,1
%A A250660 _R. H. Hardin_, Nov 26 2014