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%I #7 Nov 27 2018 12:25:30
%S 337,2058,9109,32636,100843,279718,715685,1722176,3954037,8757506,
%T 18871133,39828260,82762159,170015870,346360653,701430696,1414589161,
%U 2844655514,5709353797,11444200908,22920272755,45879723734,91806810133
%N Number of (4+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.
%H R. H. Hardin, <a href="/A251271/b251271.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 11*a(n-1) - 54*a(n-2) + 156*a(n-3) - 294*a(n-4) + 378*a(n-5) - 336*a(n-6) + 204*a(n-7) - 81*a(n-8) + 19*a(n-9) - 2*a(n-10).
%F Conjectures from _Colin Barker_, Nov 27 2018: (Start)
%F G.f.: x*(337 - 1649*x + 4669*x^2 - 9003*x^3 + 11763*x^4 - 10549*x^5 + 6447*x^6 - 2573*x^7 + 606*x^8 - 64*x^9) / ((1 - x)^9*(1 - 2*x)).
%F a(n) = (20160*(1369*2^n-1365) - 18907464*n - 6363848*n^2 - 1352064*n^3 - 190036*n^4 - 16401*n^5 - 637*n^6 + 9*n^7 + n^8) / 2520.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0..0....0..1..0..0..0....0..0..0..0..0....1..0..1..0..1
%e ..0..0..0..0..1....0..0..1..1..1....1..1..1..1..1....0..1..0..1..1
%e ..0..0..0..1..1....0..0..0..1..1....0..1..1..1..1....0..0..1..1..1
%e ..0..1..1..0..0....0..0..0..1..1....0..0..0..1..1....1..1..0..0..0
%e ..0..0..0..1..1....0..1..1..0..0....0..1..1..0..0....0..0..1..1..1
%Y Row 4 of A251268.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
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