A223319 Rolling icosahedron footprints: number of n X 6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

3125, 3570125, 4176940625, 4903804407125, 5759605530667625, 6765094542682458125, 7946162712131677450625, 9333430848774501484101125, 10962893764533341367143473625, 12876834103685350223700565272125

Offset

1,1

Comments

Column 6 of A223321.

Links

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

Formula

Empirical: a(n) = 1366*a(n-1) - 232713*a(n-2) + 9253764*a(n-3).

Empirical g.f.: 125*x*(25 - 5589*x + 219024*x^2) / (1 - 1366*x + 232713*x^2 - 9253764*x^3). - Colin Barker, Aug 19 2018

Example

Some solutions for n=3:
..0..6..0..6..0..5....0..6..0..1..8..2....0..6..0..6..0..2....0..6..0..6..0..2
..0..6..0..5..6..4....0..6..0..2..0..6....0..6..0..1..8..3....0..6..0..5..0..7
..0..1..7..5.10.11....0..1..0..2..4..8....0..1..3..9..8..3....0..1..7..1..3..7
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

Crossrefs

Cf. A223321.

Sequence in context: A017453 A017585 A223261 * A222279 A169753 A132655

Adjacent sequences: A223316 A223317 A223318 * A223320 A223321 A223322

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved