%I #9 Apr 14 2018 07:33:43

%S 28,160,918,5430,32042,188394,1107926,6519094,38356642,225665454,

%T 1327676850,7811308282,45957316482,270386512686,1590799536334,

%U 9359355830962,55065102381718,323971594861746,1906063733817962

%N Half the number of (n+1) X 3 binary arrays with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.

%C Column 2 of A184614.

%H R. H. Hardin, <a href="/A184607/b184607.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) + 3*a(n-2) + 10*a(n-3) + 29*a(n-4) - 66*a(n-5) - 20*a(n-6) + 8*a(n-7) - 12*a(n-8) + 8*a(n-9).

%F Empirical g.f.: 2*x*(14 + 10*x + 17*x^2 + 40*x^3 - 137*x^4 - 39*x^5 + 14*x^6 - 22*x^7 + 16*x^8) / (1 - 5*x - 3*x^2 - 10*x^3 - 29*x^4 + 66*x^5 + 20*x^6 - 8*x^7 + 12*x^8 - 8*x^9). - _Colin Barker_, Apr 14 2018

%e Some solutions for 4 X 3:

%e ..1..0..1....1..0..1....0..1..0....1..0..1....0..1..0....0..1..1....0..1..1

%e ..1..0..0....1..0..0....0..1..0....1..0..1....0..1..0....1..0..1....1..1..1

%e ..1..0..1....1..1..1....1..0..0....1..1..1....1..1..0....0..1..0....1..1..1

%e ..0..0..1....1..0..0....1..0..1....0..0..1....0..0..0....0..1..0....1..0..1

%e ...

%e ...2..1.......2..1.......2..2.......2..2.......2..2.......2..3.......3..4...

%e ...2..1.......3..2.......2..1.......3..3.......3..2.......2..2.......4..4...

%e ...1..2.......3..2.......2..1.......2..3.......2..1.......2..2.......3..3...

%Y Cf. A184614.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 18 2011