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Number of nX2 n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX2 n X 2 array.

Column 2 of A219471.

Empirical: a(n) = (1/20160)*n^8 + (1/1260)*n^7 + (1/480)*n^6 + (4/45)*n^5 - (11/960)*n^4 + (277/180)*n^3 + (7607/5040)*n^2 + (61/70)*n.

Conjectures from Colin Barker, Jul 26 2018: (Start)

G.f.: x*(4 - 13*x + 19*x^2 - 7*x^3 - 8*x^4 + 10*x^5 - 2*x^6 - x^7) / (1 - x)^9.

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>9.

(End)

Some solutions for n=3:

Cf. A219471.

R. H. Hardin , Nov 20 2012

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R. H. Hardin, <a href="/A219465/b219465.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX2 array

4, 23, 82, 239, 619, 1471, 3259, 6800, 13464, 25453, 46178, 80755, 136643, 224449, 358927, 560200, 855236, 1279611, 1879594, 2714591, 3859987, 5410427, 7483579, 10224424, 13810120, 18455489, 24419178, 32010547, 41597339, 53614189, 68572031

1,1

Column 2 of A219471

Empirical: a(n) = (1/20160)*n^8 + (1/1260)*n^7 + (1/480)*n^6 + (4/45)*n^5 - (11/960)*n^4 + (277/180)*n^3 + (7607/5040)*n^2 + (61/70)*n

Some solutions for n=3

..2..2....0..0....1..1....1..1....2..2....1..1....1..1....0..0....1..1....1..1

..0..0....1..1....0..0....1..1....0..0....1..1....1..1....0..1....1..1....2..2

..0..1....3..3....0..3....0..0....0..3....1..3....1..2....0..0....3..3....2..3

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nonn

R. H. Hardin Nov 20 2012

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allocated for R. H. Hardin

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