A223205 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.
27, 375, 5763, 90111, 1412907, 22163655, 347696019, 5454600015, 85571052219, 1342427863959, 21059839795875, 330384125138847, 5183024720307531, 81310641801813351, 1275591151342290099, 20011314009255431919
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0..1..6.10....0..2..3..2....0..5..9..8....0..1..0..2....0..1..4.17 ..1..0..1..6....2..3..2..3....5..9.14..9....1..6..1..0....1..0..1..4 ..4..1..6.10....3..2..3.16....9.14..9..5....0..1..0..2....4..1..6..1 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. A223209.
Formula
Empirical: a(n) = 19*a(n-1) - 54*a(n-2) + 32*a(n-3).
Empirical g.f.: 3*x*(9 - 46*x + 32*x^2) / (1 - 19*x + 54*x^2 - 32*x^3). - Colin Barker, Aug 17 2018
Comments