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%I #8 Jul 27 2018 08:56:55
%S 3,6,14,29,56,101,171,274,419,616,876,1211,1634,2159,2801,3576,4501,
%T 5594,6874,8361,10076,12041,14279,16814,19671,22876,26456,30439,34854,
%U 39731,45101,50996,57449,64494,72166,80501,89536,99309,109859,121226,133451
%N Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
%C Column 3 of A219773.
%H R. H. Hardin, <a href="/A219768/b219768.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 - (25/24)*n^2 + (23/4)*n - 4 for n>1.
%F Conjectures from _Colin Barker_, Jul 27 2018: (Start)
%F G.f.: x*(1 - 2*x + 2*x^2)*(3 - 3*x + 2*x^2 - x^3) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0
%e ..0..0..1....0..0..1....0..0..1....0..1..1....1..1..1....0..0..1....0..0..1
%e ..0..0..1....1..0..0....1..1..1....1..1..1....1..1..1....1..1..1....0..0..1
%Y Cf. A219773.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2012
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