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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A221824.
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
Comments