A223283 Rolling icosahedron face footprints: number of 2 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
20, 15, 87, 351, 1575, 6831, 29943, 130815, 572103, 2501199, 10936215, 47815839, 209064807, 914089455, 3996657207, 17474508351, 76403468295, 334057454991, 1460593174743, 6386124254175, 27921931810983, 122082540957999
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 1 4 0 1 4 0 5 0 0 1 6 0 1 0 0 5 7 0 1 6 4 1 0 4 1 4 7 5 7 0 1 4 0 5 0 9 5 0 4 1 0 Face neighbors: 0 -> 1 2 5 1 -> 0 4 6 2 -> 0 3 8 3 -> 2 4 16 4 -> 3 1 17 5 -> 0 7 9 6 -> 1 7 10 7 -> 6 5 11 8 -> 2 9 13 9 -> 8 5 14 10 -> 6 12 17 11 -> 7 12 14 12 -> 11 10 19 13 -> 8 15 16 14 -> 9 11 15 15 -> 14 13 19 16 -> 3 13 18 17 -> 4 10 18 18 -> 16 17 19 19 -> 15 18 12
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A223282.
Formula
Empirical: a(n) = 3*a(n-1) + 6*a(n-2) for n>3.
Empirical g.f.: x*(20 - 45*x - 78*x^2) / (1 - 3*x - 6*x^2). - Colin Barker, Aug 18 2018
Comments