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%I #7 Mar 11 2018 15:09:33
%S 4,13,59,181,469,1107,2447,5120,10197,19415,35485,62501,106471,175993,
%T 283101,444308,681875,1025337,1513319,2195677,3136001,4414519,6131443,
%U 8410800,11404793,15298739,20316633,26727389,34851811,45070349,57831697
%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 nonincreasing columns, 0..3 n X 2 array.
%C Column 2 of A219578.
%H R. H. Hardin, <a href="/A219572/b219572.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/20160)*n^8 + (1/2520)*n^7 + (1/480)*n^6 + (43/360)*n^5 - (297/320)*n^4 + (1271/180)*n^3 - (75973/5040)*n^2 + (2081/105)*n - 12 for n>1.
%F Conjectures from _Colin Barker_, Mar 11 2018: (Start)
%F G.f.: x*(4 - 23*x + 86*x^2 - 218*x^3 + 376*x^4 - 420*x^5 + 296*x^6 - 127*x^7 + 33*x^8 - 5*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>10.
%F (End)
%e Some solutions for n=3:
%e ..2..2....0..0....1..1....0..0....2..2....0..0....1..1....0..0....0..0....1..1
%e ..2..1....2..0....2..1....0..0....2..2....1..0....1..1....1..0....2..0....1..0
%e ..1..1....3..3....1..1....2..1....3..3....3..3....1..1....1..3....2..2....0..0
%Y Cf. A219578.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2012
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