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%I #8 Mar 11 2018 11:22:07
%S 4,13,60,193,514,1231,2748,5802,11665,22432,41419,73698,126799,211612,
%T 343525,543837,841488,1275151,1895734,2769343,3980760,5637493,7874458,
%U 10859356,14798811,19945338,26605213,35147320,46013053,59727354,76910971
%N Number of n X 2 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..3 n X 2 array.
%C Column 2 of A219373.
%H R. H. Hardin, <a href="/A219367/b219367.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/13440)*n^8 + (1/3360)*n^7 + (1/576)*n^6 + (41/240)*n^5 - (9419/5760)*n^4 + (2009/160)*n^3 - (70291/2016)*n^2 + (42649/840)*n - 29 for n>1.
%F Conjectures from _Colin Barker_, Mar 11 2018: (Start)
%F G.f.: x*(4 - 23*x + 87*x^2 - 215*x^3 + 349*x^4 - 353*x^5 + 219*x^6 - 84*x^7 + 25*x^8 - 6*x^9) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F (End)
%e Some solutions for n=3:
%e ..0..0....0..0....1..1....2..2....0..0....0..0....2..1....1..0....2..0....2..0
%e ..0..1....0..1....1..1....2..2....0..0....0..2....1..1....0..0....0..0....0..0
%e ..2..3....3..1....2..3....2..3....0..1....2..2....1..1....2..0....2..0....3..0
%Y Cf. A219373.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 19 2012