A223265 Rolling cube footprints: number of n X 4 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

64, 6144, 622592, 63438848, 6467616768, 659411697664, 67231270567936, 6854664725200896, 698877628160933888, 71255117675418877952, 7264922488410118029312, 740706078202304288260096

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Column 4 of A223269.

Examples

			Some solutions for n=3:
..0..3..5..1....0..4..2..0....0..3..0..1....0..3..5..2....0..3..4..3
..0..3..5..2....0..4..2..0....0..1..0..3....0..2..0..3....0..2..0..2
..0..2..1..2....0..4..3..4....0..1..0..4....0..3..5..3....1..2..1..2
Face neighbors:
0.->.1.2.3.4
1.->.0.2.3.5
2.->.0.1.4.5
3.->.0.1.4.5
4.->.0.3.2.5
5.->.1.3.4.2
		

Links

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

Crossrefs

Cf. A223269.

Formula

Empirical: a(n) = 112*a(n-1) - 1024*a(n-2).

Empirical g.f.: 64*x*(1 - 16*x) / (1 - 112*x + 1024*x^2). - Colin Barker, Aug 18 2018