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A250728 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 min(x(i,j),x(i-1,j)) in the j direction.

%I A250728 #6 Jul 23 2025 12:44:33
%S A250728 1302,3173,6257,11377,19887,34069,57397,95231,155263,248537,390263,
%T A250728 601256,909242,1350837,1973466,2838027,4021571,5620807,7755707,
%U A250728 10574024,14256002,19020095,25128978,32896671,42696063,54967661,70228855,89084528
%N A250728 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 min(x(i,j),x(i-1,j)) in the j direction.
%C A250728 Column 7 of A250729
%H A250728 R. H. Hardin, <a href="/A250728/b250728.txt">Table of n, a(n) for n = 1..210</a>
%F A250728 Empirical: a(n) = 8*a(n-1) -27*a(n-2) +48*a(n-3) -42*a(n-4) +42*a(n-6) -48*a(n-7) +27*a(n-8) -8*a(n-9) +a(n-10) for n>17
%F A250728 Empirical for n mod 2 = 0: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (71/1440)*n^6 + (71/120)*n^5 + (17767/2880)*n^4 + (1159/120)*n^3 + (533033/1680)*n^2 + (86336/105)*n - 5 for n>7
%F A250728 Empirical for n mod 2 = 1: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (71/1440)*n^6 + (71/120)*n^5 + (17767/2880)*n^4 + (1159/120)*n^3 + (533033/1680)*n^2 + (86336/105)*n - 17 for n>7
%e A250728 Some solutions for n=4
%e A250728 ..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..1
%e A250728 ..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..1....0..0..0..0..0..0..1..1
%e A250728 ..0..0..0..0..0..1..1..1....0..0..0..0..0..0..0..1....0..0..0..0..0..1..1..1
%e A250728 ..0..0..0..0..0..1..1..1....0..0..0..0..1..0..0..1....0..0..0..0..0..1..1..1
%e A250728 ..0..0..0..0..1..1..1..1....1..1..0..1..0..1..0..1....1..0..1..1..0..1..1..1
%K A250728 nonn
%O A250728 1,1
%A A250728 _R. H. Hardin_, Nov 27 2014