A223181 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, vertical or antidiagonal neighbor moves along an icosahedral edge.

25, 80, 400, 2080, 10880, 56960, 298240, 1561600, 8176640, 42813440, 224174080, 1173790720, 6146048000, 32181125120, 168502558720, 882290851840, 4619734876160, 24189245849600, 126656535592960, 663182230159360

Offset

1,1

Comments

Column 3 of A223186.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 4*a(n-2) for n>3.

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

G.f.: 5*x*(5 - 14*x + 4*x^2) / (1 - 6*x + 4*x^2).

a(n) = sqrt(5)*((3-sqrt(5))^n*(1+sqrt(5)) + (-1+sqrt(5))*(3+sqrt(5))^n) for n>1.

(End)

Example

Some solutions for n=3:
..0..7..1....0..2..6....0..5..7....0..2..6....0..5.10....0..6..4....0..7..1
..5..0..2....6..0..2....7.11..5....6..4..2....7.11..5....5.10..6....1..0..2
..7..1..0....2..1..0....5..7.11....2..6..4....5.10..6....6..5..0....2..1..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. A223186.

Sequence in context: A080699 A134153 A251311 * A016814 A280343 A204708

Adjacent sequences: A223178 A223179 A223180 * A223182 A223183 A223184

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved