A222015 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.
3, 27, 188, 1363, 9838, 70994, 512456, 3698699, 26696370, 192687348, 1390767557, 10038200482, 72453134112, 522947981192, 3774503253017, 27243388115499, 196635728242591, 1419265821803368, 10243893573843252, 73937773981558032
Offset: 1
Keywords
Examples
Some solutions for n=3: ..3..0....0..2....0..1....1..0....0..2....0..2....2..1....1..1....2..1....2..1 ..1..0....1..2....2..0....0..4....0..3....0..1....0..0....1..3....0..0....0..1 ..2..0....0..1....2..1....1..0....1..0....2..1....2..1....0..0....0..3....1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A222020.
Formula
Empirical: a(n) = 3*a(n-1) + 25*a(n-2) + 40*a(n-3) + a(n-4) - 42*a(n-5) - 20*a(n-6) + 10*a(n-7) + 4*a(n-8) - a(n-9).
Empirical g.f.: x*(1 + x)*(3 + 15*x + 17*x^2 - 13*x^3 - 21*x^4 + 5*x^5 + 5*x^6 - x^7) / (1 - 3*x - 25*x^2 - 40*x^3 - x^4 + 42*x^5 + 20*x^6 - 10*x^7 - 4*x^8 + x^9). - Colin Barker, Aug 14 2018
Comments