A223228 Rolling icosahedron footprints: number of n X 3 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.

25, 785, 25225, 812225, 26157625, 842416625, 27130395625, 873746350625, 28139386665625, 906241361740625, 29185902861015625, 939944877578890625, 30271339457769765625, 974901842039841640625, 31397143920195178515625

Offset

1,1

Comments

Column 3 of A223233.

Links

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

Formula

Empirical: a(n) = 35*a(n-1) - 90*a(n-2).

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

G.f.: 5*x*(5 - 18*x) / (1 - 35*x + 90*x^2).

a(n) = (2^(-1-n)*((35-sqrt(865))^n*(-15+sqrt(865)) + (15+sqrt(865))*(35+sqrt(865))^n)) / sqrt(865).

(End)

Example

Some solutions for n=3:
..0..7.11....0..7.11....0..6.10....0..7..0....0..2..0....0..2..0....0..6..4
..3..7..3....3..7..1....2..6..2...11..7..1....0..7..0....0..6..4....4..2..4
.11..7.11....5..7..3....2..4..2....0..7..5...11..7..3....4..2..0....8..9..4
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: A123835 A012835 A277584 * A132540 A337247 A142998

Adjacent sequences: A223225 A223226 A223227 * A223229 A223230 A223231

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved