A223284 Rolling icosahedron face footprints: number of 3 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.
400, 75, 849, 4995, 38457, 261819, 1881441, 13196979, 93567177, 660226923, 4668616305, 32981553891, 233097416793, 1647108262683, 11639737522305, 82252298336787, 581246168781033, 4107418513432011, 29025468445135761
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 2 3 0 1 0 0 5 7 0 5 9 0 1 0 0 1 6 0 5 9 8 2 3 6 1 4 9 5 9 0 5 9 4 1 6 0 1 4 9 5 9 8 2 3 6 1 0 7 5 9 0 5 9 6 1 4 4 1 0 7 5 9 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) = 5*a(n-1) + 18*a(n-2) - 24*a(n-3) for n>4.
Empirical g.f.: x*(400 - 1925*x - 6726*x^2 + 9000*x^3) / (1 - 5*x - 18*x^2 + 24*x^3). - Colin Barker, Aug 18 2018
Comments