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A220154 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.

%I A220154 #8 Mar 13 2018 11:13:10
%S A220154 6,11,23,50,88,137,197,268,350,443,547,662,788,925,1073,1232,1402,
%T A220154 1583,1775,1978,2192,2417,2653,2900,3158,3427,3707,3998,4300,4613,
%U A220154 4937,5272,5618,5975,6343,6722,7112,7513,7925,8348,8782,9227,9683,10150,10628
%N A220154 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.
%C A220154 Row 2 of A220153.
%H A220154 R. H. Hardin, <a href="/A220154/b220154.txt">Table of n, a(n) for n = 1..210</a>
%F A220154 Empirical: a(n) = (11/2)*n^2 - (23/2)*n + 8 for n>2.
%F A220154 Conjectures from _Colin Barker_, Mar 13 2018: (Start)
%F A220154 G.f.: x*(6 - 7*x + 8*x^2 + 8*x^3 - 4*x^4) / (1 - x)^3.
%F A220154 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F A220154 (End)
%e A220154 Some solutions for n=3
%e A220154 ..0..0..0....0..0..0....2..0..0....1..0..1....0..0..0....1..1..1....1..0..0
%e A220154 ..0..0..0....1..0..0....2..0..0....1..0..0....2..2..0....2..2..1....2..1..1
%Y A220154 Cf. A220153.
%K A220154 nonn
%O A220154 1,1
%A A220154 _R. H. Hardin_, Dec 06 2012