A223235 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

144, 845, 25225, 492365, 11043445, 236027705, 5127809545, 110781320885, 2397904326205, 51869658014705, 1122255717889585, 24279356422739885, 525283571663978725, 11364402460546714985, 245867265513538637785

Offset

1,1

Comments

Row 3 of A223233.

Links

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

Formula

Empirical: a(n) = 18*a(n-1) + 103*a(n-2) - 552*a(n-3) + 540*a(n-4) for n>5.

Empirical g.f.: x*(144 - 1747*x - 4817*x^2 + 30768*x^3 - 28620*x^4) / (1 - 18*x - 103*x^2 + 552*x^3 - 540*x^4). - Colin Barker, Aug 17 2018

Example

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

Crossrefs

Cf. A223233.

Sequence in context: A237734 A234091 A234084 * A187301 A120089 A159748

Adjacent sequences: A223232 A223233 A223234 * A223236 A223237 A223238

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved