A223323 Rolling icosahedron footprints: number of 3 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.

144, 3125, 105625, 3570125, 122039125, 4176940625, 142980696625, 4894441131125, 167544253118125, 5735298712573625, 196328142425559625, 6720615878249268125, 230057073000574997125, 7875209325727694302625, 269580591960578208870625

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Row 3 of A223321.

Examples

			Some solutions for n=3:
..0..6..5....0..7..3....0..1..8....0..7.11....0..7.11....0..7..1....0..7..1
..4.10..4....3..8..2....0..1..8....3..7..3....0..7..1....1..2..8....1..8..4
.11..9..3....1..8..1....2..1..2....3..9..8...11..3..7....0..1..7....9..8..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
		

Links

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

Crossrefs

Cf. A223321.

Formula

Empirical: a(n) = 38*a(n-1) - 129*a(n-2) for n>4.

Empirical g.f.: x*(144 - 2347*x + 5451*x^2 - 40500*x^3) / (1 - 38*x + 129*x^2). - Colin Barker, Aug 19 2018