A223204 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 or vertical neighbor moves across an icosahedral edge.

9, 75, 657, 5763, 50553, 443451, 3889953, 34122675, 299324169, 2625672171, 23032401201, 202040266467, 1772297595801, 15546597829275, 136374785271873, 1196279871788307, 10493769275551017, 92051363736382539, 807474735076340817

Offset

1,1

Comments

Column 3 of A223209.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 2*a(n-2).

Conjectures from Colin Barker, Aug 17 2018: (Start)

G.f.: 3*x*(3 - 2*x) / (1 - 9*x + 2*x^2).

a(n) = (3*2^(-1-n)*((9-sqrt(73))^n*(3+sqrt(73)) + (-3+sqrt(73))*(9+sqrt(73))^n)) / sqrt(73).

(End)

Example

Some solutions for n=3:
..0..5..0....0..5..0....0..5..7....0..1..0....0..5..9....0..5..7....0..1..4
..5..0..1....5..7..5....5..7..5....1..0..5....5..9..8....2..0..5....1..4.17
..0..5..0....9..5..9....0..5..0....4..1..0....0..5..9....0..1..0....4.17.10
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. A223209.

Sequence in context: A095249 A190983 A254664 * A351513 A136659 A231592

Adjacent sequences: A223201 A223202 A223203 * A223205 A223206 A223207

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved