%I #8 Apr 11 2018 08:46:22
%S 11,16,36,73,134,225,354,529,758,1049,1410,1849,2374,2993,3714,4545,
%T 5494,6569,7778,9129,10630,12289,14114,16113,18294,20665,23234,26009,
%U 28998,32209,35650,39329,43254,47433,51874,56585,61574,66849,72418,78289,84470
%N Number of (n+1) X 3 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 2 of A184071.
%H R. H. Hardin, <a href="/A184064/b184064.txt">Table of n, a(n) for n = 1..200</a>
%F Conjectures from _Colin Barker_, Apr 11 2018: (Start)
%F G.f.: x*(11 - 28*x + 38*x^2 - 19*x^3 + 5*x^4 - x^5 + 2*x^6) / (1 - x)^4.
%F a(n) = (4*n^3 - 15*n^2 + 74*n - 93) / 3 for n>3.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.
%F (End)
%e Some solutions for 4 X 3:
%e ..0..0..1....1..1..1....0..0..0....0..0..1....0..0..0....0..1..1....0..1..1
%e ..0..1..0....1..1..1....0..0..1....0..1..0....0..0..0....1..0..1....1..0..1
%e ..1..0..1....1..1..1....0..1..0....0..1..1....0..0..0....1..0..1....1..0..1
%e ..1..1..1....1..1..1....0..1..0....1..1..0....0..0..0....1..1..0....1..1..1
%e ...
%e ...1..2.......4..4.......0..1.......1..2.......0..0.......2..3.......2..3...
%e ...2..2.......4..4.......1..2.......2..3.......0..0.......2..2.......2..2...
%e ...3..3.......4..4.......2..2.......3..3.......0..0.......3..2.......3..3...
%Y Cf. A184071.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 09 2011