A223234 Rolling icosahedron footprints: number of 2 X n 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.

12, 65, 785, 7445, 75665, 753005, 7540985, 75377045, 753868865, 7538393405, 75384819785, 753845540645, 7538463378065, 75384609865805, 753846170402585, 7538461488792245, 75384615533623265, 753846153399130205

Offset

1,1

Comments

Row 2 of A223233.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) + 30*a(n-2) for n>3.

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

G.f.: x*(12 - 19*x - 30*x^2) / ((1 + 3*x)*(1 - 10*x)).

a(n) = (-25*(-1)^n*3^(1+n) + 49*10^n) / 65 for n>1.

(End)

Example

Some solutions for n=3:
..0..2..1....0..7.11....0..6..2....0..6..5....0..7..3....0..2..1....0..2..0
..0..7..0....3..7..3...10..6..4....4..6..5....3..7..0....6..2..8....8..2..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: A003868 A304833 A363591 * A289223 A296914 A285580

Adjacent sequences: A223231 A223232 A223233 * A223235 A223236 A223237

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved