A229446 Number of 3 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

8, 13, 22, 37, 60, 93, 138, 197, 272, 365, 478, 613, 772, 957, 1170, 1413, 1688, 1997, 2342, 2725, 3148, 3613, 4122, 4677, 5280, 5933, 6638, 7397, 8212, 9085, 10018, 11013, 12072, 13197, 14390, 15653, 16988, 18397, 19882, 21445, 23088, 24813, 26622, 28517

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/3)*n^3 + (8/3)*n + 5.

Conjectures from Colin Barker, Sep 17 2018: (Start)

G.f.: x*(8 - 19*x + 18*x^2 - 5*x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

Some solutions for n=4:
..0..2..2..2....0..0..2..2....0..2..2..2....0..0..0..2....0..0..0..2
..1..0..2..2....0..0..2..2....1..0..2..2....1..1..1..0....0..0..0..2
..2..1..0..2....1..1..0..2....2..1..0..0....1..1..1..1....0..0..0..2

Crossrefs

Row 3 of A229445.

Sequence in context: A269354 A195984 A019535 * A205704 A337212 A093023

Adjacent sequences: A229443 A229444 A229445 * A229447 A229448 A229449

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved