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Number of (3+1) X (n+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
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%I #7 Dec 12 2018 14:12:25

%S 69,73,85,120,192,336,624,1200,2352,4656,9264,18480,36912,73776,

%T 147504,294960,589872,1179696,2359344,4718640,9437232,18874416,

%U 37748784,75497520,150994992,301989936,603979824,1207959600,2415919152,4831838256

%N Number of (3+1) X (n+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

%H R. H. Hardin, <a href="/A253437/b253437.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) for n>5.

%F Empirical: a(n) = 9*2^(n-1) + 48 for n>3.

%F Empirical g.f.: x*(69 - 134*x + 4*x^2 + 11*x^3 + 2*x^4) / ((1 - x)*(1 - 2*x)). - _Colin Barker_, Dec 12 2018

%e Some solutions for n=4:

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

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

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

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

%Y Row 3 of A253435.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2014