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%I #7 Jul 27 2018 08:56:40
%S 4,9,33,100,283,732,1745,3881,8149,16288,31169,57354,101850,175100,
%T 292257,474791,752483,1165864,1769161,2633816,3852648,5544732,7861073,
%U 10991157,15170465,20689040,27901201,37236502,49212038,64446204,83674017
%N Number of n X 4 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 4 array.
%C Column 4 of A219773.
%H R. H. Hardin, <a href="/A219769/b219769.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/10080)*n^8 - (1/120)*n^6 + (73/240)*n^5 - (487/160)*n^4 + (1015/48)*n^3 - (191389/2520)*n^2 + (2351/20)*n - 5 for n>5.
%F Conjectures from _Colin Barker_, Jul 27 2018: (Start)
%F G.f.: x*(4 - 27*x + 96*x^2 - 209*x^3 + 319*x^4 - 357*x^5 + 305*x^6 - 190*x^7 + 94*x^8 - 54*x^9 + 35*x^10 - 12*x^11 - x^12 + x^13) / (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>14.
%F (End)
%e Some solutions for n=3:
%e ..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1
%e ..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..1..1
%e ..0..0..1..1....1..1..0..0....0..0..0..0....1..0..0..0....0..0..1..1
%Y Cf. A219773.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2012
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