%I
%S 3,7,17,35,62,103,165,257,390,577,833,1175,1622,2195,2917,3813,4910,
%T 6237,7825,9707,11918,14495,17477,20905,24822,29273,34305,39967,46310,
%U 53387,61253,69965,79582,90165,101777,114483,128350,143447,159845,177617
%N Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
%C Column 2 of A219299.
%H R. H. Hardin, <a href="/A219293/b219293.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/12)*n^4  (2/3)*n^3 + (53/12)*n^2  (17/6)*n  3 for n > 2.
%F Conjectures from _Colin Barker_, Jul 25 2018: (Start)
%F G.f.: x*(3  8*x + 12*x^2  10*x^3 + 2*x^4 + 5*x^5  2*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 2 2 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
%e 2 2 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0
%e 2 2 0 0 0 0 1 1 1 2 2 2 0 2 1 2 0 0 0 1
%Y Cf. A219299.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 17 2012
