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%I #4 Nov 14 2012 21:54:59
%S 6,7,37,113,345,955,2508,6303,15251,35567,80116,174791,370485,765038,
%T 1542719,3044020,5887082,11175742,20850733,38274020,69187496,
%U 123264742,216590254,375571230,643035886,1087631035,1818143164,3005088770
%N Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 nX3 array
%C Column 3 of A219217
%H R. H. Hardin, <a href="/A219212/b219212.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/20922789888000)*n^16 - (1/201180672000)*n^15 + (317/1046139494400)*n^14 - (409/37362124800)*n^13 + (28001/114960384000)*n^12 - (1031/513216000)*n^11 - (342367/7315660800)*n^10 + (3153317/1828915200)*n^9 - (2891026769/146313216000)*n^8 - (68017459/2612736000)*n^7 + (19662024383/5748019200)*n^6 - (4114129211/102643200)*n^5 + (80159944394683/435891456000)*n^4 + (166453839809/1397088000)*n^3 - (2770211114939/605404800)*n^2 + (3811038289/240240)*n - 15029 for n>11
%e Some solutions for n=3
%e ..0..0..2....0..0..0....0..0..2....1..1..1....0..0..1....1..1..2....0..0..1
%e ..0..0..1....0..0..0....0..0..2....1..0..0....0..0..1....1..1..1....0..0..0
%e ..1..1..1....1..0..0....1..1..2....1..0..0....0..0..1....1..1..1....0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 14 2012
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