A221883 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, without consecutive moves in the same direction.
3, 33, 326, 3223, 31832, 314426, 3105733, 30676867, 303010527, 2992984402, 29563182686, 292010132356, 2884328060800, 28489930453209, 281409090823688, 2779616346494657, 27455641219994600, 271192906082774221
Offset: 1
Keywords
Examples
Some solutions for n=3: ..1..2....0..3....0..3....0..2....1..0....0..1....1..1....1..1....1..0....0..1 ..0..0....0..1....0..3....0..2....1..1....2..0....0..2....1..0....3..1....3..1 ..0..3....0..2....0..0....2..0....1..2....0..3....0..2....0..3....1..0....0..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..55
Crossrefs
Cf. A221886.
Formula
Empirical: a(n) = 7*a(n-1) + 27*a(n-2) + 16*a(n-3) - 18*a(n-4) - 13*a(n-5) + 5*a(n-6) + 3*a(n-7) - a(n-8).
Empirical g.f.: x*(3 + 12*x + 14*x^2 + 2*x^3 - 5*x^4 - 2*x^5 + x^6) / (1 - 7*x - 27*x^2 - 16*x^3 + 18*x^4 + 13*x^5 - 5*x^6 - 3*x^7 + x^8). - Colin Barker, Aug 11 2018
Comments