A219500 Number of n X 6 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..1 n X 6 array.

6, 11, 35, 88, 179, 325, 550, 885, 1369, 2050, 2986, 4246, 5911, 8075, 10846, 14347, 18717, 24112, 30706, 38692, 48283, 59713, 73238, 89137, 107713, 129294, 154234, 182914, 215743, 253159, 295630, 343655, 397765, 458524, 526530, 602416, 686851

Offset

1,1

Comments

Column 6 of A219502.

Links

R. H. Hardin, Table of n, a(n) for n = 1..67

Formula

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (13/24)*n^3 + (59/24)*n^2 + (59/20)*n - 17 for n>3.

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

G.f.: x*(6 - 25*x + 59*x^2 - 77*x^3 + 46*x^4 - 10*x^6 + x^7 + x^8) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.

(End)

Example

Some solutions for n=3:
..1..1..1..0..0..0....1..1..1..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
..1..1..1..1..0..0....1..1..1..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
..1..1..1..1..1..0....1..1..1..0..0..0....0..0..0..0..0..0....1..1..1..1..0..0

Crossrefs

Cf. A219502.

Sequence in context: A193866 A152987 A100093 * A166702 A130667 A259669

Adjacent sequences: A219497 A219498 A219499 * A219501 A219502 A219503

Keyword

nonn

Author

R. H. Hardin, Nov 20 2012

Status

approved