A223182 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.

125, 320, 2080, 14560, 103520, 738720, 5274720, 37664800, 268947680, 1920431520, 13712917600, 97917648160, 699184991200, 4992559175840, 35649574015840, 254557248560160, 1817676496339680, 12979193733707680, 92678466337073760

Offset

1,1

Comments

Column 4 of A223186.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 25*a(n-2) + 36*a(n-3) - 24*a(n-4) + 4*a(n-5) for n>6.

Empirical g.f.: 5*x*(25 - 186*x + 401*x^2 - 548*x^3 + 280*x^4 - 36*x^5) / ((1 - x)*(1 - 9*x + 16*x^2 - 20*x^3 + 4*x^4)). - Colin Barker, Aug 17 2018

Example

Some solutions for n=3:
..0..5..7.11....0..5.10.11....0..5..7..0....0..6..2..0....0..5.10.11
..7.11..3..7....7.11..5.10....7.11..5..7....2..0..1..7....7.11..9.10
..5..7..1..3....5..7.11..5....3..7..0..5....1..7..0..1....5.10..4..9
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. A223186.

Sequence in context: A172460 A338469 A253226 * A256362 A175486 A250579

Adjacent sequences: A223179 A223180 A223181 * A223183 A223184 A223185

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved