A223229 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

125, 7445, 492365, 32837285, 2191464605, 146259564725, 9761484584045, 651489782832965, 43480983274973885, 2901957882023749205, 193679142376194109325, 12926311034495639900645, 862713015509641940473565

Offset

1,1

Comments

Column 4 of A223233.

Links

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

Formula

Empirical: a(n) = 73*a(n-1) - 423*a(n-2) + 351*a(n-3).

Empirical g.f.: 5*x*(25 - 336*x + 351*x^2) / ((1 - x)*(1 - 72*x + 351*x^2)). - Colin Barker, Aug 17 2018

Example

Some solutions for n=3:
..0..6.10..5....0..5..7..0....0..5..0..7....0..1..7..5....0..2..4..2
..0..6.10..6....0..5..7..3....6..5..0..6....0..1..7..5....6..2..8..9
..0..6..5..6....0..5..7..3....0..2..0..5....3..1..7..0....0..2..8..1
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. A223233.

Sequence in context: A017583 A046232 A102076 * A030695 A317981 A223259

Adjacent sequences: A223226 A223227 A223228 * A223230 A223231 A223232

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved