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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 columns, 0..2 n X 2 array.
2

%I #8 Mar 11 2018 10:09:13

%S 3,7,23,53,103,182,302,478,728,1073,1537,2147,2933,3928,5168,6692,

%T 8542,10763,13403,16513,20147,24362,29218,34778,41108,48277,56357,

%U 65423,75553,86828,99332,113152,128378,145103,163423,183437,205247,228958,254678

%N 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 columns, 0..2 n X 2 array.

%C Column 2 of A219173.

%H R. H. Hardin, <a href="/A219167/b219167.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/8)*n^4 - (3/4)*n^3 + (55/8)*n^2 - (49/4)*n + 8 for n>1.

%F Conjectures from _Colin Barker_, Mar 11 2018: (Start)

%F G.f.: x*(3 - 8*x + 18*x^2 - 22*x^3 + 13*x^4 - x^5) / (1 - x)^5.

%F 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 (End)

%e Some solutions for n=3:

%e ..1..1....0..0....0..0....1..0....1..1....0..0....1..1....2..2....0..0....1..1

%e ..1..1....0..0....0..0....0..0....1..1....0..0....1..1....2..2....0..1....1..1

%e ..2..1....2..2....2..0....2..0....1..2....1..2....1..1....2..2....2..1....2..2

%Y Cf. A219173.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2012