A186843 - OEIS

%I #8 Apr 19 2018 06:21:17

%S 50,218,970,4194,18246,79778,347530,1514138,6603034,28783358,

%T 125459410,546925146,2384168474,10392867762,45304600806,197491613026,

%U 860900508458,3752824392746,16359260883466,71313013661214,310866547441298

%N Number of (n+1) X 3 binary 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 2 of A186850.

%H R. H. Hardin, <a href="/A186843/b186843.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 24*a(n-3) + 14*a(n-4) + 3*a(n-5) + 2*a(n-6).

%F Empirical g.f.: 2*x*(25 + 59*x + 167*x^2 + 91*x^3 + 23*x^4 + 14*x^5) / (1 - 2*x - 4*x^2 - 24*x^3 - 14*x^4 - 3*x^5 - 2*x^6). - _Colin Barker_, Apr 19 2018

%e Some solutions for 5 X 3:

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

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

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

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

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

%Y Cf. A186850.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 27 2011