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Number of 3 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.
1

%I #9 Aug 27 2018 06:04:42

%S 8,27,58,106,175,269,392,548,741,975,1254,1582,1963,2401,2900,3464,

%T 4097,4803,5586,6450,7399,8437,9568,10796,12125,13559,15102,16758,

%U 18531,20425,22444,24592,26873,29291,31850,34554,37407,40413,43576,46900,50389,54047

%N Number of 3 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.

%C Row 3 of A224133.

%H R. H. Hardin, <a href="/A224134/b224134.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (2/3)*n^3 + (5/2)*n^2 + (35/6)*n for n>1.

%F Conjectures from _Colin Barker_, Aug 27 2018: (Start)

%F G.f.: x*(8 - 5*x - 2*x^2 + 4*x^3 - x^4) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A224133.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013