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A250661 Number of (7+1) X (n+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 A250661 #7 Nov 16 2018 05:57:01
%S A250661 639,1150,1789,2556,3451,4474,5625,6904,8311,9846,11509,13300,15219,
%T A250661 17266,19441,21744,24175,26734,29421,32236,35179,38250,41449,44776,
%U A250661 48231,51814,55525,59364,63331,67426,71649,76000,80479,85086,89821,94684,99675
%N A250661 Number of (7+1) X (n+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 A250661 R. H. Hardin, <a href="/A250661/b250661.txt">Table of n, a(n) for n = 1..210</a>
%F A250661 Empirical: a(n) = 64*n^2 + 319*n + 256.
%F A250661 Conjectures from _Colin Barker_, Nov 16 2018: (Start)
%F A250661 G.f.: x*(639 - 767*x + 256*x^2) / (1 - x)^3.
%F A250661 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250661 (End)
%e A250661 Some solutions for n=4:
%e A250661 ..1..1..1..1..1....1..1..0..0..0....1..1..0..0..0....0..0..0..0..0
%e A250661 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A250661 ..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
%e A250661 ..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A250661 ..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....1..1..1..1..1
%e A250661 ..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..1
%e A250661 ..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..1
%e A250661 ..0..0..0..0..0....0..0..1..1..1....1..1..1..1..1....0..0..0..0..1
%Y A250661 Row 7 of A250656.
%K A250661 nonn
%O A250661 1,1
%A A250661 _R. H. Hardin_, Nov 26 2014