%I #7 Oct 23 2018 11:57:12
%S 81,316,1256,4984,19900,78144,311512,1227648,4896848,19273664,
%T 76861056,302658560,1207072128,4752337152,18952790656,74623190528,
%U 297608324608,1171752619008,4673101527552,18399231225856,73378645568512
%N Number of (n+1) X (1+1) 0..2 arrays with the upper median plus the lower median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.
%H R. H. Hardin, <a href="/A237560/b237560.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n2) + 140*a(n4) + 632*a(n6) + 864*a(n8) for n>9.
%F Empirical g.f.: x*(81 + 316*x + 932*x^2 + 3720*x^3 + 3536*x^4 + 13968*x^5 + 4880*x^6 + 17600*x^7 + 1024*x^8) / (1  4*x^2  140*x^4  632*x^6  864*x^8).  _Colin Barker_, Oct 23 2018
%e Some solutions for n=5:
%e ..1..0....2..0....2..0....0..1....0..2....2..0....0..2....0..1....0..1....2..0
%e ..2..0....2..1....0..0....2..0....2..2....2..0....2..1....1..2....0..0....1..2
%e ..2..0....1..0....2..1....2..0....0..1....2..1....2..2....0..0....2..1....0..1
%e ..1..0....1..0....0..1....2..1....1..2....0..1....1..1....0..2....1..1....0..1
%e ..1..2....2..1....2..2....2..2....0..0....2..0....0..1....1..0....0..0....1..2
%e ..2..1....0..2....1..2....1..0....1..0....0..0....0..1....1..2....0..0....2..1
%Y Column 1 of A237567.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 09 2014
