A223329 Rolling cube footprints: number of n X 6 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.

243, 64827, 17324685, 4630596579, 1237689159021, 330815891296611, 88422165323034669, 23633929115222765283, 6316997592145707860589, 1688439462802532886238947, 451294745322310558858483245

Offset

1,1

Comments

Column 6 of A223331.

Links

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

Formula

Empirical: a(n) = 282*a(n-1) - 3969*a(n-2) + 9604*a(n-3).

Empirical g.f.: 27*x*(9 - 137*x + 294*x^2) / (1 - 282*x + 3969*x^2 - 9604*x^3). - Colin Barker, Aug 19 2018

Example

Some solutions for n=3:
..0..4..0..4..6..2....0..4..0..1..0..1....0..4..6..7..5..1....0..4..0..1..5..4
..0..4..0..2..0..2....0..4..5..4..5..4....0..4..5..4..0..1....0..4..5..4..6..7
..0..4..6..4..0..2....0..4..5..4..5..4....0..4..5..4..0..2....0..4..5..4..5..7
Vertex neighbors:
0 -> 1 2 4
1 -> 0 3 5
2 -> 0 3 6
3 -> 1 2 7
4 -> 0 5 6
5 -> 1 4 7
6 -> 2 4 7
7 -> 3 5 6

Crossrefs

Cf. A223331.

Sequence in context: A223792 A223978 A223573 * A216328 A086649 A184691

Adjacent sequences: A223326 A223327 A223328 * A223330 A223331 A223332

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved