A223333 Rolling cube footprints: number of 4 X n 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.

512, 2187, 83349, 3176523, 121264857, 4630596579, 176834343105, 6753068175483, 257891143282857, 9848539671395859, 376103406869296785, 14362918587487614123, 548501892736263190137, 20946601106278812695619

Offset

1,1

Links

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

Formula

Empirical: a(n) = 48*a(n-1) - 402*a(n-2) + 1064*a(n-3) - 789*a(n-4) for n>7.

Empirical g.f.: x*(512 - 22389*x + 184197*x^2 - 489823*x^3 + 375051*x^4 - 112104*x^5 + 121716*x^6) / ((1 - 3*x)*(1 - 45*x + 267*x^2 - 263*x^3)). - Colin Barker, Aug 19 2018

Example

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

Row 4 of A223331.

Sequence in context: A203451 A251192 A251187 * A135273 A258522 A258519

Adjacent sequences: A223330 A223331 A223332 * A223334 A223335 A223336

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved