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Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
1

%I #8 Dec 12 2018 09:40:07

%S 109,102,120,156,228,372,660,1236,2388,4692,9300,18516,36948,73812,

%T 147540,294996,589908,1179732,2359380,4718676,9437268,18874452,

%U 37748820,75497556,150995028,301989972,603979860,1207959636,2415919188,4831838292

%N Number of (n+1) X (4+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="/A253431/b253431.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>3.

%F Empirical: a(n) = 9*2^(n-1) + 84 for n>1.

%F Empirical g.f.: x*(109 - 225*x + 32*x^2) / ((1 - x)*(1 - 2*x)). - _Colin Barker_, Dec 12 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A253435.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2014