A223318 Rolling icosahedron footprints: number of n X 5 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.

625, 274625, 122039125, 54279694625, 24143758634125, 10739266230499625, 4776881955584279125, 2124782217358970404625, 945114307570509938324125, 420391815800244320602909625, 186992491150169573406883769125

Offset

1,1

Comments

Column 5 of A223321.

Links

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

Formula

Empirical: a(n) = 479*a(n-1) - 15210*a(n-2).

Conjectures from Colin Barker, Aug 19 2018: (Start)

G.f.: 125*x*(5 - 198*x) / (1 - 479*x + 15210*x^2).

a(n) = (25*2^(-1-n)*((479-sqrt(168601))^n*(-3181+11*sqrt(168601)) + (479+sqrt(168601))^n*(3181+11*sqrt(168601)))) / (169*sqrt(168601)).

(End)

Example

Some solutions for n=3:
..0..6..2..6.10....0..6..2..6..0....0..6.10..6..0....0..6..0..1..3
..0..6..0..6..2....0..6..0..6..2....0..6..0..2..4....0..6..2..8..2
..0..1..0..1..3....0..1..2..1..0....0..2..4.10..4....0..1..2..4..8
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: A223260 A350430 A187456 * A222278 A120320 A013837

Adjacent sequences: A223315 A223316 A223317 * A223319 A223320 A223321

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved