A184606 - OEIS

%I #11 Apr 14 2018 07:33:45

%S 8,28,98,350,1250,4450,15842,56426,200978,715786,2549282,9079418,

%T 32336882,115169482,410182082,1460885210,5203020050,18530830570,

%U 65998531298,235057255034,837168828722,2981620996234,10619200644098

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

%C Column 1 of A184614.

%H R. H. Hardin, <a href="/A184606/b184606.txt">Table of n, a(n) for n = 1..200</a>

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

%F Empirical g.f.: 2*x*(4 + 2*x + 7*x^2 + 4*x^3) / ((1 + 2*x^2)*(1 - 3*x - 2*x^2)). - _Colin Barker_, Apr 14 2018

%e Some solutions for 3 X 2:

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

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

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

%e ...

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

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

%Y Cf. A184614.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 18 2011