A219514 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.

3, 4, 11, 22, 42, 74, 124, 199, 307, 457, 659, 924, 1264, 1692, 2222, 2869, 3649, 4579, 5677, 6962, 8454, 10174, 12144, 14387, 16927, 19789, 22999, 26584, 30572, 34992, 39874, 45249, 51149, 57607, 64657, 72334, 80674, 89714, 99492, 110047, 121419

Offset

1,1

Comments

Column 3 of A219519.

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 - (37/24)*n^2 + (161/12)*n - 23 for n>3.

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

G.f.: x*(3 - 11*x + 21*x^2 - 23*x^3 + 17*x^4 - 9*x^5 + 5*x^6 - 2*x^7) / (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>8.

(End)

Example

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

Crossrefs

Cf. A219519.

Sequence in context: A001643 A247171 A005218 * A131481 A001072 A292623

Adjacent sequences: A219511 A219512 A219513 * A219515 A219516 A219517

Keyword

nonn

Author

R. H. Hardin, Nov 21 2012

Status

approved