A222160 Number of (n+2) X 1 arrays of occupancy after each element moves up to +-2 places but not 0 and without 2-loops.

1, 5, 17, 53, 159, 467, 1356, 3913, 11253, 32299, 92606, 265353, 760080, 2176758, 6233232, 17847997, 51103477, 146319703, 418938535, 1199485661, 3434300229, 9832876386, 28152852451, 80605364957, 230783807849, 660764392260

Offset

1,2

Comments

Column 2 of A222165.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3) - 2*a(n-4) - 2*a(n-5) - a(n-6).

Empirical g.f.: x*(1 + x)^2 / ((1 - x - x^2)*(1 - 2*x - 2*x^2 - x^3 - x^4)). - Colin Barker, Aug 15 2018

Example

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

Crossrefs

Cf. A222165.

Sequence in context: A110318 A088210 A135344 * A027028 A176086 A154992

Adjacent sequences: A222157 A222158 A222159 * A222161 A222162 A222163

Keyword

nonn

Author

R. H. Hardin, Feb 10 2013

Status

approved