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A250858 Number of (6+1) X (n+1) 0..3 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 A250858 #8 Nov 22 2018 06:33:23
%S A250858 233683,1280447,4648157,13263136,32201019,69543783,137379337,
%T A250858 252943672,439905571,729793879,1163567333,1793326952,2684170987,
%U A250858 3916192431,5586619089,7812096208,10731111667,14506563727,19328471341,25416827024
%N A250858 Number of (6+1) X (n+1) 0..3 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 A250858 R. H. Hardin, <a href="/A250858/b250858.txt">Table of n, a(n) for n = 1..60</a>
%F A250858 Empirical: a(n) = 198*n^6 + (35807/12)*n^5 + (204911/12)*n^4 + (214827/4)*n^3 + (998209/12)*n^2 + (180451/3)*n + 16384.
%F A250858 Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F A250858 G.f.: x*(233683 - 355334*x + 592371*x^2 - 563481*x^3 + 333624*x^4 - 114687*x^5 + 16384*x^6) / (1 - x)^7.
%F A250858 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A250858 (End)
%e A250858 Some solutions for n=1.
%e A250858 ..2..2....0..0....2..0....2..2....0..0....0..0....2..2....2..2....2..2....0..0
%e A250858 ..0..0....2..2....0..0....3..3....1..1....0..0....1..1....1..1....1..1....1..1
%e A250858 ..3..3....3..3....2..2....0..0....3..3....2..2....1..1....1..1....0..0....0..0
%e A250858 ..3..3....1..3....3..3....2..2....2..2....1..1....1..1....1..1....1..1....0..0
%e A250858 ..2..2....0..2....0..1....1..3....2..2....1..1....3..3....2..2....2..2....0..2
%e A250858 ..0..0....0..3....2..3....0..2....1..2....3..3....3..3....1..1....0..3....0..2
%e A250858 ..0..1....0..3....2..3....1..3....1..3....1..3....0..1....0..2....0..3....0..3
%Y A250858 Row 6 of A250853.
%K A250858 nonn
%O A250858 1,1
%A A250858 _R. H. Hardin_, Nov 28 2014