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A250781 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 absolute value of x(i,j)-x(i-1,j) in the j direction.

%I A250781 #7 Nov 19 2018 11:42:02
%S A250781 436,1106,2604,5882,12950,27986,59590,125334,260916,538538,1103752,
%T A250781 2249266,4562698,9222258,18588322,37386830,75076376,150582730,
%U A250781 301768276,604371338,1209885342,2421317714,4844708318,9692167046,19387949788
%N A250781 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 absolute value of x(i,j)-x(i-1,j) in the j direction.
%H A250781 R. H. Hardin, <a href="/A250781/b250781.txt">Table of n, a(n) for n = 1..210</a>
%F A250781 Empirical: a(n) = 10*a(n-1) - 44*a(n-2) + 112*a(n-3) - 182*a(n-4) + 196*a(n-5) - 140*a(n-6) + 64*a(n-7) - 17*a(n-8) + 2*a(n-9).
%F A250781 Conjectures from _Colin Barker_, Nov 19 2018: (Start)
%F A250781 G.f.: 2*x*(218 - 1627*x + 5364*x^2 - 10163*x^3 + 12093*x^4 - 9259*x^5 + 4469*x^6 - 1253*x^7 + 160*x^8) / ((1 - x)^8*(1 - 2*x)).
%F A250781 a(n) = (2520*(289*2^n-209) - 314796*n - 41972*n^2 - 23779*n^3 + 385*n^4 - 364*n^5 + 7*n^6 - n^7) / 1260.
%F A250781 (End)
%e A250781 Some solutions for n=4:
%e A250781 ..1..1..0..0..0..0..1....0..0..0..0..0..1..0....0..0..1..1..0..0..0
%e A250781 ..1..1..0..0..0..0..1....0..1..1..1..1..0..1....0..0..1..1..0..0..1
%e A250781 ..1..1..0..0..0..0..1....0..1..1..1..1..1..0....0..0..1..1..0..0..1
%e A250781 ..1..1..0..0..0..0..1....0..1..1..1..1..1..0....0..0..1..1..0..1..0
%e A250781 ..1..1..0..0..0..1..0....0..1..1..1..1..1..0....0..0..1..1..0..1..1
%Y A250781 Column 6 of A250783.
%K A250781 nonn
%O A250781 1,1
%A A250781 _R. H. Hardin_, Nov 27 2014