A240701 Number of n X 3 0..3 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

2, 27, 461, 7980, 138562, 2406061, 41780245, 725496762, 12597953186, 218758280685, 3798647658637, 65961955769536, 1145402258889550, 19889439592325187, 345371946166981361, 5997241935624779340

Offset

1,1

Links

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

Formula

Empirical: a(n) = 15*a(n-1) + 40*a(n-2) + 22*a(n-3) - 60*a(n-4) - 40*a(n-5) - 21*a(n-6) + 45*a(n-7).

Empirical g.f.: x*(2 - 3*x - 24*x^2 - 59*x^3 - 52*x^4 - 11*x^5 + 72*x^6) / ((1 - x)*(1 + x + x^2)*(1 - 15*x - 40*x^2 - 21*x^3 + 45*x^4)). - Colin Barker, Oct 29 2018

Example

Some solutions for n=4:
..0..1..0....0..1..0....0..1..2....0..1..2....0..1..0....0..1..2....0..1..0
..2..3..1....1..2..3....3..0..3....1..0..3....2..0..2....3..2..1....2..3..1
..0..1..3....0..0..1....1..2..0....2..2..0....0..1..3....2..0..3....0..1..2
..1..0..2....0..0..3....3..1..2....2..2..1....2..3..0....3..1..2....1..2..0

Crossrefs

Column 3 of A240706.

Sequence in context: A277832 A221674 A363961 * A240638 A245050 A242009

Adjacent sequences: A240698 A240699 A240700 * A240702 A240703 A240704

Keyword

nonn

Author

R. H. Hardin, Apr 10 2014

Status

approved