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A219590 Number of n X 3 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..2 n X 3 array.

%I A219590 #7 Jul 26 2018 09:25:55
%S A219590 6,18,84,264,705,1739,4129,9518,21271,46019,96412,195879,386603,
%T A219590 742477,1389545,2537385,4526097,7895059,13481452,22558778,37028253,
%U A219590 59679103,94537481,147328016,226076963,341891611,509957092,750799089,1091869239
%N A219590 Number of n X 3 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..2 n X 3 array.
%C A219590 Column 3 of A219595.
%H A219590 R. H. Hardin, <a href="/A219590/b219590.txt">Table of n, a(n) for n = 1..210</a>
%F A219590 Empirical: a(n) = (1/13305600)*n^11 + (1/1814400)*n^10 - (1/48384)*n^9 + (67/120960)*n^8 - (1009/403200)*n^7 + (403/86400)*n^6 + (106961/241920)*n^5 - (1857341/362880)*n^4 + (10083109/302400)*n^3 - (4379099/50400)*n^2 + (889043/9240)*n - 17 for n>2.
%F A219590 Conjectures from _Colin Barker_, Jul 26 2018: (Start)
%F A219590 G.f.: x*(6 - 54*x + 264*x^2 - 876*x^3 + 2091*x^4 - 3619*x^5 + 4579*x^6 - 4324*x^7 + 3206*x^8 - 1982*x^9 + 1025*x^10 - 397*x^11 + 93*x^12 - 9*x^13) / (1 - x)^12.
%F A219590 a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>14.
%F A219590 (End)
%e A219590 Some solutions for n=3:
%e A219590 ..0..0..0....1..1..0....0..0..0....1..0..0....2..1..1....1..0..0....1..0..0
%e A219590 ..1..0..0....1..0..0....1..0..0....1..1..0....2..2..1....2..1..0....2..1..0
%e A219590 ..2..0..0....2..0..0....1..2..0....1..1..1....2..2..2....2..2..1....2..2..2
%Y A219590 Cf. A219595.
%K A219590 nonn
%O A219590 1,1
%A A219590 _R. H. Hardin_, Nov 23 2012