A223258 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 or vertical neighbor moves along an icosahedral edge.

25, 845, 28885, 988625, 33841585, 1158447605, 39655444525, 1357467150905, 46468199390665, 1590678314378525, 54451378224988165, 1863954869994720545, 63806057268775907425, 2184179997984165531845, 74767858535726198152285

Offset

1,1

Comments

Column 3 of A223263.

Links

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

Formula

Empirical: a(n) = 38*a(n-1) - 129*a(n-2).

Conjectures from Colin Barker, Aug 18 2018: (Start)

G.f.: 5*x*(5 - 21*x) / (1 - 38*x + 129*x^2).

a(n) = (5*((19-2*sqrt(58))^n*(-41+7*sqrt(58)) + (19+2*sqrt(58))^n*(41+7*sqrt(58)))) / (86*sqrt(58)).

(End)

Example

Some solutions for n=3:
..0..1..3....0..6..2....0..5..6....0..1..8....0..7..1....0..7..1....0..2..8
..6..2..8....5.10..6....5.10..5....1..0..2....6..5..0....7..1..3....1..8..4
..2..0..2...10..6..2....7..5..7....7..5..0....2..0..1....5..7.11....8..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. A223263.

Sequence in context: A251925 A181892 A274469 * A209119 A350983 A224478

Adjacent sequences: A223255 A223256 A223257 * A223259 A223260 A223261

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved