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%I #8 Apr 11 2018 08:10:24
%S 7,11,20,34,54,81,116,160,214,279,356,446,550,669,804,956,1126,1315,
%T 1524,1754,2006,2281,2580,2904,3254,3631,4036,4470,4934,5429,5956,
%U 6516,7110,7739,8404,9106,9846,10625,11444,12304,13206,14151,15140,16174,17254
%N Number of (n+1) X 2 binary arrays with rows and columns in nondecreasing order and with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.
%C Column 1 of A184071.
%H R. H. Hardin, <a href="/A184063/b184063.txt">Table of n, a(n) for n = 1..200</a>
%F Conjectures from _Colin Barker_, Apr 11 2018: (Start)
%F G.f.: x*(7 - 17*x + 18*x^2 - 8*x^3 + x^4) / (1 - x)^4.
%F a(n) = (n^3 + 6*n^2 + 5*n + 24) / 6 for n>1.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F (End)
%e Some solutions for 3 X 2:
%e ..0..0....0..1....0..0....0..1....0..0....0..1....0..0....0..1....0..1....0..1
%e ..0..1....0..1....0..0....1..1....0..0....1..0....0..1....0..1....1..0....0..1
%e ..1..0....1..0....0..1....1..1....0..0....1..1....0..1....1..1....1..0....0..1
%e ...
%e ...1.......2.......0.......3.......0.......2.......1.......2.......2.......2...
%e ...2.......2.......1.......4.......0.......3.......2.......3.......2.......2...
%Y Cf. A184071.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 09 2011
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