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%I #7 Jul 26 2018 06:37:01
%S 4,5,24,68,187,465,1090,2430,5181,10575,20714,39046,71023,124990,
%T 213360,354136,572847,904971,1398924,2119700,3153253,4611718,6639574,
%U 9420858,13187545,18229215,24904134,33651882,45007667,59618470,78261172
%N Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.
%C Column 4 of A219519.
%H R. H. Hardin, <a href="/A219515/b219515.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/6720)*n^8 - (1/360)*n^7 + (41/1440)*n^6 + (7/18)*n^5 - (41099/2880)*n^4 + (68651/360)*n^3 - (6724661/5040)*n^2 + (58709/12)*n - 7380 for n>6.
%F Conjectures from _Colin Barker_, Jul 26 2018: (Start)
%F G.f.: x*(4 - 31*x + 123*x^2 - 304*x^3 + 523*x^4 - 660*x^5 + 655*x^6 - 528*x^7 + 357*x^8 - 217*x^9 + 156*x^10 - 128*x^11 + 74*x^12 - 15*x^13 - 3*x^14) / (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>15.
%F (End)
%e Some solutions for n=3:
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0
%e ..0..0..1..0....1..0..1..1....1..0..1..0....1..1..1..1....0..0..0..1
%Y Cf. A219519.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 21 2012
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