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%I #8 Dec 22 2018 07:29:01
%S 44,112,210,344,506,683,894,1140,1421,1725,2071,2460,2892,3355,3868,
%T 4432,5047,5701,6413,7184,8014,8891,9834,10844,11921,13053,14259,
%U 15540,16896,18315,19816,21400,23067,24805,26633,28552,30562,32651,34838,37124,39509
%N Number of (2+1) X (n+1) 0..1 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.
%H R. H. Hardin, <a href="/A258555/b258555.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7) for n>10.
%F Empirical g.f.: x*(44 - 20*x + 6*x^2 + 6*x^3 - 52*x^4 + 7*x^5 + 13*x^6 - 5*x^7 + 8*x^8 + x^9) / ((1 - x)^4*(1 + x)*(1 + x^2)). - _Colin Barker_, Dec 22 2018
%e Some solutions for n=4:
%e ..1..0..0..1..1....1..0..0..0..1....1..0..0..0..0....1..0..0..1..1
%e ..1..0..0..0..0....1..0..0..0..0....1..0..0..0..1....0..0..1..1..1
%e ..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..1..1..0..1
%Y Row 2 of A258554.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 03 2015
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