%I #8 Jul 25 2018 08:16:36
%S 3,6,19,42,79,136,220,339,502,719,1001,1360,1809,2362,3034,3841,4800,
%T 5929,7247,8774,10531,12540,14824,17407,20314,23571,27205,31244,35717,
%U 40654,46086,52045,58564,65677,73419,81826,90935,100784,111412,122859
%N Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
%C Column 3 of A219291.
%H R. H. Hardin, <a href="/A219286/b219286.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3  (1/24)*n^2 + (27/4)*n  11 for n>2.
%F Conjectures from _Colin Barker_, Jul 25 2018: (Start)
%F G.f.: x*(3  9*x + 19*x^2  23*x^3 + 14*x^4  2*x^5  x^6) / (1  x)^5.
%F a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) for n>7.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1....0..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e ..0..0..1....0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
%e ..0..1..1....0..0..0....1..0..0....0..1..0....1..1..1....0..0..1....0..0..1
%Y Cf. A219291.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 17 2012
