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Number of nX3 n X 3 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..1 nX3 n X 3 array.

Column 3 of A219291.

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 - (1/24)*n^2 + (27/4)*n - 11 for n>2.

Conjectures from Colin Barker, Jul 25 2018: (Start)

G.f.: x*(3 - 9*x + 19*x^2 - 23*x^3 + 14*x^4 - 2*x^5 - x^6) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.

(End)

Some solutions for n=3:

Cf. A219291.

R. H. Hardin , Nov 17 2012

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R. H. Hardin, <a href="/A219286/b219286.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX3 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..1 nX3 array

3, 6, 19, 42, 79, 136, 220, 339, 502, 719, 1001, 1360, 1809, 2362, 3034, 3841, 4800, 5929, 7247, 8774, 10531, 12540, 14824, 17407, 20314, 23571, 27205, 31244, 35717, 40654, 46086, 52045, 58564, 65677, 73419, 81826, 90935, 100784, 111412, 122859

1,1

Column 3 of A219291

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 - (1/24)*n^2 + (27/4)*n - 11 for n>2

Some solutions for n=3

..0..0..1....0..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

..0..0..1....0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1

..0..1..1....0..0..0....1..0..0....0..1..0....1..1..1....0..0..1....0..0..1

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nonn

R. H. Hardin Nov 17 2012

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