A219286 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.

3, 6, 19, 42, 79, 136, 220, 339, 502, 719, 1001, 1360, 1809, 2362, 3034, 3841, 4800, 5929, 7247, 8774, 10531, 12540, 14824, 17407, 20314, 23571, 27205, 31244, 35717, 40654, 46086, 52045, 58564, 65677, 73419, 81826, 90935, 100784, 111412, 122859

Offset

1,1

Comments

Column 3 of A219291.

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 - (1/24)*n^2 + (27/4)*n - 11 for n>2.

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

G.f.: x*(3 - 9*x + 19*x^2 - 23*x^3 + 14*x^4 - 2*x^5 - x^6) / (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>7.

(End)

Example

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

Crossrefs

Cf. A219291.

Sequence in context: A203797 A019097 A347685 * A104264 A007098 A226322

Adjacent sequences: A219283 A219284 A219285 * A219287 A219288 A219289

Keyword

nonn

Author

R. H. Hardin, Nov 17 2012

Status

approved