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A219589 Number of n X 2 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 2 array.

%I A219589 #8 Mar 12 2018 09:41:04
%S A219589 3,7,21,46,87,151,247,386,581,847,1201,1662,2251,2991,3907,5026,6377,
%T A219589 7991,9901,12142,14751,17767,21231,25186,29677,34751,40457,46846,
%U A219589 53971,61887,70651,80322,90961,102631,115397,129326,144487,160951,178791
%N A219589 Number of n X 2 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 2 array.
%C A219589 Column 2 of A219595.
%H A219589 R. H. Hardin, <a href="/A219589/b219589.txt">Table of n, a(n) for n = 1..210</a>
%F A219589 Empirical: a(n) = (1/12)*n^4 - (1/3)*n^3 + (47/12)*n^2 - (14/3)*n + 2 for n>1.
%F A219589 Conjectures from _Colin Barker_, Mar 12 2018: (Start)
%F A219589 G.f.: x*(3 - 8*x + 16*x^2 - 19*x^3 + 12*x^4 - 2*x^5) / (1 - x)^5.
%F A219589 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F A219589 (End)
%e A219589 Some solutions for n=3:
%e A219589 ..0..0....0..0....0..0....1..0....0..0....1..1....0..0....2..2....1..0....0..0
%e A219589 ..1..0....2..0....0..0....0..0....1..0....1..1....0..0....2..2....0..0....0..0
%e A219589 ..1..1....2..2....1..1....1..0....0..0....2..1....2..0....2..2....2..0....0..0
%Y A219589 Cf. A219595.
%K A219589 nonn
%O A219589 1,1
%A A219589 _R. H. Hardin_, Nov 23 2012