A223481 Rolling icosahedron face footprints: number of 3 X n 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.

400, 243, 2025, 16875, 147825, 1296675, 11374425, 99776475, 875239425, 7677601875, 67347938025, 590776238475, 5182290270225, 45459059955075, 398766959055225, 3497984511586875, 30684326686171425, 269162971152369075

Offset

1,1

Comments

Row 3 of A223480.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 2*a(n-2) for n>4.

Empirical g.f.: x*(400 - 3357*x + 638*x^2 - 864*x^3) / (1 - 9*x + 2*x^2). - Colin Barker, Aug 20 2018

Example

Some solutions for n=3:
..0..2..3....0..1..0....0..2..8....0..5..0....0..1..0....0..2..0....0..1..6
..3..4..1....0..2..8....3..2..8....0..5..9....0..2..0....3..2..3....6..1..6
..1..4..1....8..2..8....8..9..5....9..8..2....3..2..8....3..4..1....6.10.12
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

Crossrefs

Cf. A223480.

Sequence in context: A356821 A223284 A061042 * A037991 A200837 A250847

Adjacent sequences: A223478 A223479 A223480 * A223482 A223483 A223484

Keyword

nonn

Author

R. H. Hardin, Mar 20 2013

Status

approved