A223322 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 or antidiagonal neighbor moves along an icosahedral edge.

12, 125, 1625, 21125, 274625, 3570125, 46411625, 603351125, 7843564625, 101966340125, 1325562421625, 17232311481125, 224020049254625, 2912260640310125, 37859388324031625, 492172048212411125

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Row 2 of A223321.

Examples

			Some solutions for n=3:
..0..7..3....0..2..8....0..2..4....0..5.11....0..6..5....0..1..3....0..7..0
..1..8..4....8..1..2....8..2..1...10..9..4....2..6..2....3.11..3....0..1..7
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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (13).

Crossrefs

Cf. A223321.

Formula

Empirical: a(n) = 13*a(n-1) for n>2.

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

G.f.: x*(12 - 31*x) / (1 - 13*x).

a(n) = 125*13^(n-2) for n>1.

(End)