A223478 Rolling icosahedron face footprints: number of n X 6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

243, 16875, 1296675, 101331675, 7939566675, 622332801675, 48783753036675, 3824122400271675, 299770559674506675, 23498831496975741675, 1842059141815703976675, 144397899075877259211675

Offset: 1

Author

R. H. Hardin, Mar 20 2013

Keywords

• nonn

Comments

Column 6 of A223480.

Examples

			Some solutions for n=3:
..0..1..6..1..4..3....0..1..4..1..4..1....0..1..0..5..9..8....0..1..0..2..3.16
..0..1..0..1..4..1....0..1..4..1..4..3....0..5..9..5..9..5....0..2..0..2..3.16
..0..1..4..1..6..1....6..1..4..3..2..0....0..5..9.14..9.14....0..2..3..4..3..4
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12
		

Links

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

Crossrefs

Cf. A223480.

Formula

Empirical: a(n) = 101*a(n-1) -1900*a(n-2) +10000*a(n-3).

Empirical g.f.: 27*x*(9 - 284*x + 2000*x^2) / (1 - 101*x + 1900*x^2 - 10000*x^3). - Colin Barker, Aug 20 2018