A219699 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.

3, 5, 13, 25, 45, 78, 130, 208, 320, 475, 683, 955, 1303, 1740, 2280, 2938, 3730, 4673, 5785, 7085, 8593, 10330, 12318, 14580, 17140, 20023, 23255, 26863, 30875, 35320, 40228, 45630, 51558, 58045, 65125, 72833, 81205, 90278, 100090, 110680, 122088

Offset

1,1

Comments

Column 3 of A219704.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (25/24)*n^2 + (107/12)*n - 10 for n>1.

Conjectures from Colin Barker, Jul 27 2018: (Start)

G.f.: x*(3 - 10*x + 18*x^2 - 20*x^3 + 15*x^4 - 5*x^5) / (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>6.

(End)

Example

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

Crossrefs

Cf. A219704.

Sequence in context: A027305 A026766 A026709 * A320330 A159290 A110494

Adjacent sequences: A219696 A219697 A219698 * A219700 A219701 A219702

Keyword

nonn

Author

R. H. Hardin, Nov 25 2012

Status

approved