%I
%S 50,228,928,3574,13346,48848,176420,631130,2242678,7930164,27941848,
%T 98196574,344438730,1206482520,4221685708,14761290914,51584989022,
%U 180196526268,629274809856,2197047322662,7669531252530,26769919917152
%N Number of (n+1) X (2+1) 0..1 arrays with the difference of the upper and lower median value of each 2 X 2 subblock in lexicographically nondecreasing order columnwise and nonincreasing rowwise.
%H R. H. Hardin, <a href="/A235956/b235956.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n1)  16*a(n2)  22*a(n3) + 105*a(n4)  66*a(n5)  120*a(n6) + 176*a(n7)  64*a(n8).
%F Empirical g.f.: 2*x*(25  86*x  48*x^2 + 449*x^3  316*x^4  480*x^5 + 704*x^6  256*x^7) / ((1  x)^2*(1  2*x)*(1  x  4*x^2)*(1  3*x  4*x^2 + 8*x^3)).  _Colin Barker_, Oct 20 2018
%e Some solutions for n=4:
%e ..0..0..1....0..1..0....0..1..0....0..0..1....1..0..1....1..0..0....1..0..1
%e ..0..0..1....0..0..1....1..0..1....0..0..1....1..1..0....0..0..1....0..1..0
%e ..1..0..1....1..0..1....1..0..1....1..0..1....0..1..1....0..1..1....1..1..1
%e ..1..1..0....1..1..0....0..0..1....1..1..0....1..1..1....1..1..0....1..1..1
%e ..1..1..0....1..0..0....1..0..0....1..0..1....0..1..1....1..1..1....0..1..0
%Y Column 2 of A235962.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 17 2014
