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Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock two extreme terms minus its two median terms lexicographically nondecreasing rowwise and columnwise.
2

%I #8 Mar 19 2018 10:35:57

%S 16,46,120,288,660,1456,3136,6624,13808,28480,58304,118656,240448,

%T 485632,978432,1967616,3951360,7926784,15889408,31832064,63742976,

%U 127602688,255377408,511008768,1022390272,2045329408,4091461632,8184102912

%N Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock two extreme terms minus its two median terms lexicographically nondecreasing rowwise and columnwise.

%C Column 1 of A235555.

%H R. H. Hardin, <a href="/A235549/b235549.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3) - 4*a(n-4) + 8*a(n-5).

%F Empirical g.f.: 2*x*(8 + 7*x - 18*x^2 - 4*x^3 + 18*x^4) / ((1 - 2*x)*(1 - 2*x^2)^2). - _Colin Barker_, Mar 19 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Cf. A235555.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 12 2014