A223271 Rolling cube footprints: number of 3 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.

36, 576, 20992, 622592, 19726336, 611319808, 19084083200, 594316099584, 18523120205824, 577157705236480, 17985124012392448, 560427673747193856, 17463446426942963712, 544175431737222889472, 16956974709073621549056

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Row 3 of A223269.

Examples

			Some solutions for n=3:
..0..2..5....0..2..1....0..1..0....0..1..0....0..1..5....0..2..0....0..1..5
..0..2..0....4..3..1....0..3..0....5..3..5....0..1..0....5..1..0....0..3..5
..4..3..4....0..2..1....0..4..5....4..2..0....2..4..3....0..3..5....5..3..1
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) = 24*a(n-1) + 256*a(n-2) - 1024*a(n-3) for n>4.

Empirical g.f.: 4*x*(9 - 72*x - 512*x^2 + 2048*x^3) / (1 - 24*x - 256*x^2 + 1024*x^3). - Colin Barker, Aug 18 2018