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A219687 Number of 3 X n 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 nonincreasing columns, 0..2 3 X n array.

%I A219687 #8 Jul 26 2018 15:17:01
%S A219687 6,9,31,87,208,452,922,1799,3394,6234,11196,19713,34085,57937,96878,
%T A219687 159429,258304,412146,647840,1003547,1532627,2308645,3431682,5036203,
%U A219687 7300766,10459890,14818436,20768893,28812001,39581185,53871318,72672377
%N A219687 Number of 3 X n 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 nonincreasing columns, 0..2 3 X n array.
%C A219687 Row 3 of A219686.
%H A219687 R. H. Hardin, <a href="/A219687/b219687.txt">Table of n, a(n) for n = 1..210</a>
%F A219687 Empirical: a(n) = (1/181440)*n^9 - (1/4032)*n^8 + (31/4320)*n^7 - (37/288)*n^6 + (14137/8640)*n^5 - (7859/576)*n^4 + (3420947/45360)*n^3 - (240133/1008)*n^2 + (63709/180)*n - 79 for n>6.
%F A219687 Conjectures from _Colin Barker_, Jul 26 2018: (Start)
%F A219687 G.f.: x*(6 - 51*x + 211*x^2 - 538*x^3 + 913*x^4 - 1055*x^5 + 824*x^6 - 413*x^7 + 110*x^8 + 8*x^9 - 27*x^10 + 23*x^11 - 12*x^12 + x^13 + 3*x^14 - x^15) / (1 - x)^10.
%F A219687 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>15.
%F A219687 (End)
%e A219687 Some solutions for n=3:
%e A219687 ..2..0..0....1..0..0....2..1..1....1..0..0....1..0..0....2..0..0....1..1..1
%e A219687 ..2..0..0....0..0..0....2..1..1....1..0..0....1..0..0....2..0..0....1..1..1
%e A219687 ..2..2..2....0..0..2....2..2..2....1..1..2....2..2..2....2..0..0....1..1..1
%Y A219687 Cf. A219686.
%K A219687 nonn
%O A219687 1,1
%A A219687 _R. H. Hardin_, Nov 25 2012