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%I #8 Apr 12 2018 03:49:05
%S 29,58,150,335,728,1499,2968,5645,10331,18242,31173,51709,83492,
%T 131554,202727,306142,453830,661439,949082,1342332,1873381,2582381,
%U 3518986,4744115,6331957,8372240,10972787,14262383,18393978,23548252,29937569
%N Number of (n+1) X 2 0..2 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 A184081.
%H R. H. Hardin, <a href="/A184073/b184073.txt">Table of n, a(n) for n = 1..200</a>
%F Conjectures from _Colin Barker_, Apr 12 2018: (Start)
%F G.f.: x*(29 - 203*x + 672*x^2 - 1363*x^3 + 1895*x^4 - 1939*x^5 + 1573*x^6 - 1117*x^7 + 749*x^8 - 450*x^9 + 209*x^10 - 65*x^11 + 12*x^12 - x^13) / (1 - x)^9.
%F a(n) = (1290240 - 1768560*n + 1559788*n^2 - 343756*n^3 + 72569*n^4 - 4480*n^5 + 602*n^6 - 4*n^7 + n^8) / 40320 for n>5.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>14.
%F (End)
%e Some solutions for 3 X 2:
%e ..0..0....0..1....0..2....0..2....0..0....0..2....0..2....0..1....0..1....0..1
%e ..0..1....0..2....1..0....1..1....0..2....2..0....2..0....0..1....1..1....0..1
%e ..0..1....1..0....2..0....2..0....1..0....2..1....2..0....0..2....1..1....1..1
%e ...
%e ...1.......3.......3.......4.......2.......4.......4.......2.......3.......2...
%e ...2.......3.......3.......4.......3.......5.......4.......3.......4.......3...
%Y Cf. A184081.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 09 2011