A223278 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

27, 351, 4995, 72279, 1048923, 15229647, 221142771, 3211159815, 46628577099, 677084057343, 9831800199267, 142765577323191, 2073070007320635, 30102629340815919, 437114178530327763, 6347246378746198887

Offset

1,1

Comments

Column 4 of A223282.

Links

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

Formula

Empirical: a(n) = 17*a(n-1) - 36*a(n-2).

Conjectures from Colin Barker, Aug 18 2018: (Start)

G.f.: 27*x*(1 - 4*x) / (1 - 17*x + 36*x^2).

a(n) = (3*2^(-1-n)*((17-sqrt(145))^n*(-1+sqrt(145)) + (1+sqrt(145))*(17+sqrt(145))^n)) / sqrt(145).

(End)

Example

Some solutions for n=3:
..0..2..3.16....0..2..0..1....0..1..0..1....0..2..0..1....0..5..0..1
..8..2..3..2....0..5..0..1....4..1..4..1....0..1..0..5....0..2..0..1
..3..2..3.16....7..5..0..5....4..1..6..1....4..1..0..5....3..2..0..5
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. A223282.

Sequence in context: A010943 A022622 A030648 * A278091 A042410 A110207

Adjacent sequences: A223275 A223276 A223277 * A223279 A223280 A223281

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved