A221689 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without consecutive moves in the same direction.

6, 152, 3112, 63676, 1302720, 26650988, 545221260, 11154026300, 228186749552, 4668196767064, 95500991265668, 1953739262283024, 39969188300499044, 817681276128120100, 16727952148700884996, 342216938625170086928

Offset

1,1

Comments

Column 3 of A221693.

Links

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

Formula

Empirical: a(n) = 24*a(n-1) - 69*a(n-2) - 71*a(n-3) + 2*a(n-4) for n>5.

Empirical g.f.: 2*x*(3 + 4*x - 61*x^2 - 49*x^3 + 2*x^4) / (1 - 24*x + 69*x^2 + 71*x^3 - 2*x^4). - Colin Barker, Aug 10 2018

Example

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

Crossrefs

Cf. A221693.

Sequence in context: A147796 A003766 A278728 * A354752 A319036 A185211

Adjacent sequences: A221686 A221687 A221688 * A221690 A221691 A221692

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved