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A250727 Number of (n+1) X (6+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 A250727 #7 Nov 16 2018 07:51:24
%S A250727 579,1376,2699,4889,8514,14437,23941,38821,61554,95438,144820,215289,
%T A250727 313964,449751,633699,879329,1203066,1624648,2167642,2859941,3734372,
%U A250727 4829289,6189281,7865869,9918322,12414466,15431616,19057505,23391340
%N A250727 Number of (n+1) X (6+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 A250727 R. H. Hardin, <a href="/A250727/b250727.txt">Table of n, a(n) for n = 1..210</a>
%F A250727 Empirical: a(n) = 7*a(n-1) - 20*a(n-2) + 28*a(n-3) - 14*a(n-4) - 14*a(n-5) + 28*a(n-6) - 20*a(n-7) + 7*a(n-8) - a(n-9) for n>14.
%F A250727 Empirical for n mod 2 = 0: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (179/720)*n^5 + (427/144)*n^4 + (4559/720)*n^3 + (41227/360)*n^2 + (81253/210)*n + 25 for n>5.
%F A250727 Empirical for n mod 2 = 1: a(n) = (1/2520)*n^7 + (11/720)*n^6 + (179/720)*n^5 + (427/144)*n^4 + (4559/720)*n^3 + (41227/360)*n^2 + (81253/210)*n + 27 for n>5.
%F A250727 Empirical g.f.: x*(579 - 2677*x + 4647*x^2 - 2696*x^3 - 2151*x^4 + 4417*x^5 - 2892*x^6 + 866*x^7 - 72*x^8 - 19*x^9 + 9*x^10 - 15*x^11 + 10*x^12 - 2*x^13) / ((1 - x)^8*(1 + x)). - _Colin Barker_, Nov 16 2018
%e A250727 Some solutions for n=4:
%e A250727 ..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
%e A250727 ..1..0..1..0..1..0..1....0..0..0..0..0..0..0....0..0..0..0..0..0..1
%e A250727 ..0..1..0..1..0..1..0....0..0..0..0..0..0..0....0..0..0..0..0..1..0
%e A250727 ..1..0..1..0..1..0..1....1..0..0..1..1..1..1....0..0..0..0..1..0..1
%e A250727 ..0..1..0..1..0..1..1....0..1..1..1..1..1..1....1..0..0..1..0..1..0
%Y A250727 Column 6 of A250729.
%K A250727 nonn
%O A250727 1,1
%A A250727 _R. H. Hardin_, Nov 27 2014