A223270 Rolling cube footprints: number of 2 X n 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.

6, 48, 576, 6144, 67584, 737280, 8060928, 88080384, 962592768, 10519314432, 114957484032, 1256277934080, 13728862961664, 150031797583872, 1639577995444224, 17917641486237696, 195807627744116736

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Row 2 of A223269.

Examples

			Some solutions for n=3:
..0..2..0....0..2..1....0..3..4....0..2..4....0..2..0....0..1..2....0..4..2
..5..3..4....4..3..1....4..2..4....1..3..1....1..3..5....2..4..3....0..1..0
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) = 8*a(n-1) + 32*a(n-2).

Conjectures from Colin Barker, Aug 18 2018: (Start)

G.f.: 6*x / (1 - 8*x - 32*x^2).

a(n) = (sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n)) / 4.

(End)