A219349 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.

3, 3, 8, 15, 27, 46, 76, 122, 190, 287, 421, 601, 837, 1140, 1522, 1996, 2576, 3277, 4115, 5107, 6271, 7626, 9192, 10990, 13042, 15371, 18001, 20957, 24265, 27952, 32046, 36576, 41572, 47065, 53087, 59671, 66851, 74662, 83140, 92322, 102246, 112951

Offset

1,1

Comments

Column 3 of A219354.

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 + (23/24)*n^2 + (13/4)*n - 8 for n > 3.

Conjectures from Colin Barker, Jul 25 2018: (Start)

G.f.: x*(3 - 12*x + 23*x^2 - 25*x^3 + 17*x^4 - 7*x^5 + 3*x^6 - 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:
  0 0 0   0 0 0   0 0 0   0 0 1   0 0 0   1 1 1   0 0 1
  0 0 0   0 0 0   0 0 0   0 0 1   0 0 0   1 1 1   0 0 1
  0 0 0   0 0 1   1 1 1   1 1 1   1 0 0   1 1 1   0 0 1

Crossrefs

Cf. A219354.

Sequence in context: A126592 A055057 A154029 * A208964 A104864 A300367

Adjacent sequences: A219346 A219347 A219348 * A219350 A219351 A219352

Keyword

nonn

Author

R. H. Hardin, Nov 18 2012

Status

approved