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A253226 Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically. 1

%I

%S 125,306,494,914,1709,3241,6231,12122,23800,47037,93377,185908,370806,

%T 740423,1479463,2957334,5912852,11823649,23644989,47287400,94571938,

%U 189140715,378277955,756552106,1513100064,3026195621,6052386361

%N Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.

%H R. H. Hardin, <a href="/A253226/b253226.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>8.

%F Conjectures from _Colin Barker_, Dec 10 2018: (Start)

%F G.f.: x*(125 - 319*x + 89*x^2 + 323*x^3 - 307*x^4 + 76*x^5 - 3*x^6 + x^7) / ((1 - x)^3*(1 - 2*x)).

%F a(n) = 46 + 1443*2^(n-5) + (13*n)/2 + (15*n^2)/2 for n>4.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A253231.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 29 2014

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Last modified October 3 12:48 EDT 2022. Contains 357237 sequences. (Running on oeis4.)