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A219884 Number of 3 X n 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 nonincreasing columns, 0..2 3 X n array.

%I A219884 #7 Jul 28 2018 12:27:45
%S A219884 10,21,47,129,292,600,1158,2148,3863,6784,11679,19763,32938,54144,
%T A219884 87860,140803,222883,348483,538145,820756,1236342,1839593,2704258,
%U A219884 3928566,5641847,8012546,11257843,15655113,21555482,29399758,39737040,53246333
%N A219884 Number of 3 X n 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 nonincreasing columns, 0..2 3 X n array.
%C A219884 Row 3 of A219883.
%H A219884 R. H. Hardin, <a href="/A219884/b219884.txt">Table of n, a(n) for n = 1..210</a>
%F A219884 Empirical: a(n) = (1/362880)*n^9 - (1/13440)*n^8 + (17/12096)*n^7 - (37/2880)*n^6 + (1813/17280)*n^5 + (1579/5760)*n^4 - (76849/9072)*n^3 + (768487/10080)*n^2 - (590021/2520)*n + 217 for n>6.
%F A219884 Conjectures from _Colin Barker_, Jul 28 2018: (Start)
%F A219884 G.f.: x*(10 - 79*x + 287*x^2 - 596*x^3 + 697*x^4 - 265*x^5 - 504*x^6 + 984*x^7 - 895*x^8 + 565*x^9 - 351*x^10 + 273*x^11 - 206*x^12 + 112*x^13 - 36*x^14 + 5*x^15) / (1 - x)^10.
%F A219884 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>16.
%F A219884 (End)
%e A219884 Some solutions for n=3:
%e A219884 ..1..0..0....1..0..0....0..0..0....0..0..0....1..1..1....1..0..0....0..0..0
%e A219884 ..1..0..1....1..0..1....0..0..0....0..0..0....1..0..1....1..0..0....0..0..0
%e A219884 ..2..1..2....1..0..0....2..2..2....2..1..2....1..0..0....1..0..1....0..1..0
%Y A219884 Cf. A219883.
%K A219884 nonn
%O A219884 1,1
%A A219884 _R. H. Hardin_, Nov 30 2012