A221821 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without consecutive moves in the same direction.

3, 31, 252, 2113, 17684, 147920, 1237439, 10351593, 86594795, 724396370, 6059833949, 50692672540, 424062286786, 3547432284249, 29675536361423, 248246446379403, 2076670068892280, 17372085836189001, 145323694322280832

Offset

1,1

Comments

Column 2 of A221824.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 4*a(n-2) - 11*a(n-3) - 2*a(n-4) + 22*a(n-5) - 16*a(n-6) + 8*a(n-7).

Empirical g.f.: x*(3 + 4*x - 15*x^2 + 2*x^3 + 22*x^4 - 16*x^5 + 8*x^6) / (1 - 9*x + 4*x^2 + 11*x^3 + 2*x^4 - 22*x^5 + 16*x^6 - 8*x^7). - Colin Barker, Aug 11 2018

Example

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

Crossrefs

Cf. A221824.

Sequence in context: A334980 A111400 A057972 * A198852 A114849 A221899

Adjacent sequences: A221818 A221819 A221820 * A221822 A221823 A221824

Keyword

nonn

Author

R. H. Hardin, Jan 26 2013

Status

approved