A223477 Rolling icosahedron face footprints: number of n X 5 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.

81, 3375, 147825, 6526575, 288507825, 12755926575, 563999907825, 24937217326575, 1102598111307825, 48751338478726575, 2155538829022707825, 95307078736540126575, 4213999366856734107825, 186321844088731401526575

Offset

1,1

Comments

Column 5 of A223480.

Links

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

Formula

Empirical: a(n) = 51*a(n-1) - 300*a(n-2).

Empirical g.f.: 27*x*(3 - 28*x) / (1 - 51*x + 300*x^2). - Colin Barker, Aug 20 2018

Example

Some solutions for n=3:
..0..1..6.10.17....0..1..6..7..5....0..2..0..2..0....0..2..0..1..6
..6.10.17.10.12....6..7.11..7..6....8..2..0..5..7....0..1..0..1..4
.17.10.12.11.12....6..7..5..7..5....0..5..7.11.14....0..5..0..1..6
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: A017744 A232945 A345005 * A237842 A223501 A053108

Adjacent sequences: A223474 A223475 A223476 * A223478 A223479 A223480

Keyword

nonn

Author

R. H. Hardin, Mar 20 2013

Status

approved