A223277 Rolling icosahedron face footprints: number of n X 3 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.

9, 87, 849, 8295, 81057, 792087, 7740273, 75637959, 739134273, 7222821495, 70581425169, 689721818919, 6739962906081, 65862930139863, 643612676665521, 6289384281642375, 61459874978079873, 600586013379170103

Offset

1,1

Comments

Column 3 of A223282.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 11*a(n-1) - 12*a(n-2).

Conjectures from Colin Barker, Aug 18 2018: (Start)

G.f.: 3*x*(3 - 4*x) / (1 - 11*x + 12*x^2).

a(n) = (2^(-1-n)*((11-sqrt(73))^n*(-7+sqrt(73)) + (7+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).

(End)

Example

Some solutions for n=3:
..0..2..3....0..2..3....0..1..4....0..5..9....0..1..6....0..2..0....0..5..9
..0..2..3....8..2..3....0..1..4....0..5..0....0..1..0....3..2..8....9..5..9
..0..2..8....0..2..8....0..1..4....0..1..0....4..1..4....3..2..8....0..5..7
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

Crossrefs

Cf. A223282.

Sequence in context: A219123 A144852 A153191 * A267265 A152264 A035101

Adjacent sequences: A223274 A223275 A223276 * A223278 A223279 A223280

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved