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

1,1

Comments

Column 4 of A223209.

Links

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

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

Example

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

Crossrefs

Cf. A223209.

Sequence in context: A278091 A042410 A110207 * A257786 A161530 A161954

Adjacent sequences: A223202 A223203 A223204 * A223206 A223207 A223208

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved