A219768 Number of n X 3 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..1 n X 3 array.

3, 6, 14, 29, 56, 101, 171, 274, 419, 616, 876, 1211, 1634, 2159, 2801, 3576, 4501, 5594, 6874, 8361, 10076, 12041, 14279, 16814, 19671, 22876, 26456, 30439, 34854, 39731, 45101, 50996, 57449, 64494, 72166, 80501, 89536, 99309, 109859, 121226, 133451

Offset

1,1

Comments

Column 3 of A219773.

Links

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

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 - (25/24)*n^2 + (23/4)*n - 4 for n>1.

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

G.f.: x*(1 - 2*x + 2*x^2)*(3 - 3*x + 2*x^2 - x^3) / (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..1....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0
..0..0..1....0..0..1....0..0..1....0..1..1....1..1..1....0..0..1....0..0..1
..0..0..1....1..0..0....1..1..1....1..1..1....1..1..1....1..1..1....0..0..1

Crossrefs

Cf. A219773.

Sequence in context: A308448 A055890 A306884 * A038359 A038360 A216714

Adjacent sequences: A219765 A219766 A219767 * A219769 A219770 A219771

Keyword

nonn

Author

R. H. Hardin, Nov 27 2012

Status

approved