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A250780 Number of (n+1) X (5+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 A250780 #8 Nov 19 2018 09:14:08
%S A250780 209,518,1194,2640,5688,12036,25126,51904,106344,216500,438614,885336,
%T A250780 1782168,3580356,7182678,14395024,28829560,57711060,115489574,
%U A250780 231065768,462241608,924621732,1849416198,3699045984,7398353992,14797027060
%N A250780 Number of (n+1) X (5+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 A250780 R. H. Hardin, <a href="/A250780/b250780.txt">Table of n, a(n) for n = 1..210</a>
%F A250780 Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 50*a(n-3) - 55*a(n-4) + 36*a(n-5) - 13*a(n-6) + 2*a(n-7).
%F A250780 Conjectures from _Colin Barker_, Nov 19 2018: (Start)
%F A250780 G.f.: x*(209 - 1154*x + 2693*x^2 - 3376*x^3 + 2401*x^4 - 922*x^5 + 153*x^6) / ((1 - x)^6*(1 - 2*x)).
%F A250780 a(n) = (9/2)*(49*2^n-32) - (374*n)/5 - 9*n^2 - (25*n^3)/6 - n^5/30.
%F A250780 (End)
%e A250780 Some solutions for n=4:
%e A250780 ..1..0..0..0..1..0....0..0..1..0..0..0....1..0..0..0..0..0....0..1..0..0..0..0
%e A250780 ..1..0..0..1..0..1....0..0..1..0..0..0....1..0..0..0..0..1....0..1..0..0..0..1
%e A250780 ..1..0..1..0..1..0....0..0..1..0..0..0....1..0..0..0..0..1....0..1..0..0..1..0
%e A250780 ..1..0..1..1..0..1....0..0..1..0..0..0....1..0..0..0..0..1....0..1..0..0..1..0
%e A250780 ..1..0..1..1..0..1....0..0..1..0..0..1....1..1..1..1..1..0....1..0..1..1..0..1
%Y A250780 Column 5 of A250783.
%K A250780 nonn
%O A250780 1,1
%A A250780 _R. H. Hardin_, Nov 27 2014