A223197 Rolling cube footprints: number of n X 3 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

16, 576, 20992, 765952, 27951104, 1020002304, 37222350848, 1358333739008, 49568888651776, 1808888827478016, 66010735351693312, 2408891644150546432, 87906291641005113344, 3207913535188934590464, 117064536077508729110528

Offset

1,1

Comments

Column 3 of A223202.

Links

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

Formula

Empirical: a(n) = 40*a(n-1) - 128*a(n-2).

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: 16*x*(1 - 4*x) / (1 - 40*x + 128*x^2).

a(n) = ((20-4*sqrt(17))^n*(-3+sqrt(17)) + (3+sqrt(17))*(4*(5+sqrt(17)))^n) / (4*sqrt(17)).

(End)

Example

Some solutions for n=3:
..0..1..0....0..1..5....0..3..4....0..4..5....0..3..4....0..1..5....0..3..1
..2..0..3....2..5..2....1..0..2....1..5..1....3..0..2....1..2..1....3..4..3
..0..2..0....5..1..5....5..2..1....5..1..2....4..2..4....0..4..0....4..3..1
Face neighbors:
0,5 -> 1 2 3 4
1,4 -> 0 2 3 5
2,3 -> 0 1 4 5

Crossrefs

Cf. A223202.

Sequence in context: A268566 A189147 A063082 * A089156 A210829 A222845

Adjacent sequences: A223194 A223195 A223196 * A223198 A223199 A223200

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved