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%I #9 Apr 17 2018 06:18:28
%S 81,630,4942,38700,303212,2375550,18611050,145808838,1142339588,
%T 8949663042,70116185140,549325551516,4303693552406,33717306885174,
%U 264158394384970,2069550147728712,16213900082399138,127027874230202640
%N Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock diagonal sum less antidiagonal sum equal to any horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.
%C Column 1 of A185856.
%H R. H. Hardin, <a href="/A185848/b185848.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) + 20*a(n-2) + 99*a(n-3) + 252*a(n-4) + 510*a(n-5) + 324*a(n-6) - 336*a(n-7) - 288*a(n-8).
%F Empirical g.f.: x*(81 + 387*x + 1432*x^2 + 3255*x^3 + 5490*x^4 + 2586*x^5 - 4068*x^6 - 3024*x^7) / (1 - 3*x - 20*x^2 - 99*x^3 - 252*x^4 - 510*x^5 - 324*x^6 + 336*x^7 + 288*x^8). - _Colin Barker_, Apr 17 2018
%e Some solutions for 3 X 2:
%e ..2..1....0..2....2..0....2..0....0..1....2..0....0..1....1..2....1..1....0..0
%e ..0..2....1..0....0..2....0..0....2..1....0..1....2..1....0..2....1..1....2..1
%e ..0..1....1..1....1..0....1..1....2..2....1..1....1..0....1..2....2..0....2..1
%Y Cf. A185856.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2011
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