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A250782 Number of (n+1) X (7+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 A250782 #8 Nov 19 2018 12:57:27
%S A250782 901,2326,5568,12796,28692,63184,137082,293588,621664,1303276,2708612,
%T A250782 5587548,11454008,23356632,47422730,95949660,193592124,389742628,
%U A250782 783299900,1572215204,3152596828,6316933760,12650561098,25324612868
%N A250782 Number of (n+1) X (7+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 A250782 R. H. Hardin, <a href="/A250782/b250782.txt">Table of n, a(n) for n = 1..210</a>
%F A250782 Empirical: a(n) = 12*a(n-1) - 65*a(n-2) + 210*a(n-3) - 450*a(n-4) + 672*a(n-5) - 714*a(n-6) + 540*a(n-7) - 285*a(n-8) + 100*a(n-9) - 21*a(n-10) + 2*a(n-11).
%F A250782 Conjectures from _Colin Barker_, Nov 19 2018: (Start)
%F A250782 G.f.: x*(901 - 8486*x + 36221*x^2 - 92040*x^3 + 154050*x^4 - 177432*x^5 + 142536*x^6 - 79028*x^7 + 29083*x^8 - 6482*x^9 + 681*x^10) / ((1 - x)^10*(1 - 2*x)).
%F A250782 a(n) = (45360*(3025*2^n-2344) - 70509024*n - 9423432*n^2 - 6541100*n^3 + 254142*n^4 - 151725*n^5 + 6552*n^6 - 870*n^7 + 18*n^8 - n^9) / 90720.
%F A250782 (End)
%e A250782 Some solutions for n=4:
%e A250782 ..0..0..1..1..0..0..1..0....0..0..1..0..0..0..0..1....0..0..0..0..0..1..0..1
%e A250782 ..0..0..1..1..0..0..1..0....0..0..1..0..0..0..1..0....0..0..0..0..0..1..1..0
%e A250782 ..0..0..1..1..0..0..1..0....0..0..1..0..0..1..0..1....0..0..0..0..0..1..1..0
%e A250782 ..0..0..1..1..0..1..0..1....0..0..1..0..1..0..1..0....0..0..0..0..0..1..1..1
%e A250782 ..0..0..1..1..0..1..1..0....0..0..1..1..0..1..0..1....0..0..0..0..0..1..1..1
%Y A250782 Column 7 of A250783.
%K A250782 nonn
%O A250782 1,1
%A A250782 _R. H. Hardin_, Nov 27 2014