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%I #7 Jul 30 2018 10:05:49
%S 4,10,38,103,245,547,1168,2395,4724,8982,16504,29381,50797,85475,
%T 140254,224821,352624,541994,817506,1211611,1766573,2536747,3591236,
%U 5016967,6922228,9440710,12736100,17007273,22494133,29484155,38319682,49406033
%N Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X 2 array.
%C Column 2 of A220204.
%H R. H. Hardin, <a href="/A220198/b220198.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/20160)*n^8 - (1/5040)*n^7 - (1/480)*n^6 + (107/720)*n^5 - (1151/960)*n^4 + (278/45)*n^3 - (54427/5040)*n^2 + (5323/420)*n - 7 for n>1.
%F Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F G.f.: x*(4 - 26*x + 92*x^2 - 215*x^3 + 350*x^4 - 386*x^5 + 277*x^6 - 119*x^7 + 29*x^8 - 4*x^9) / (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>10.
%F (End)
%e Some solutions for n=3:
%e ..0..0....0..0....2..2....2..2....3..3....0..0....0..0....0..0....0..0....0..0
%e ..0..0....0..0....3..2....0..0....3..3....0..0....0..0....0..0....3..0....1..0
%e ..2..0....1..1....3..3....0..0....3..3....3..3....3..1....3..2....3..3....2..2
%Y Cf. A220204.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 07 2012
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