A219465 Number of 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 n X 2 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

Offset

1,1

Comments

Column 2 of A219471.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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)

Example

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

Crossrefs

Cf. A219471.

Sequence in context: A304305 A316204 A305771 * A317120 A220647 A014585

Adjacent sequences: A219462 A219463 A219464 * A219466 A219467 A219468

Keyword

nonn

Author

R. H. Hardin, Nov 20 2012

Status

approved