A223198 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 or vertical neighbor moves across a corresponding cube edge.

64, 6912, 765952, 85327872, 9515827200, 1061444124672, 118404195287040, 13208119651860480, 1473383170773614592, 164357898631630553088, 18334348775748242767872, 2045221757767217986928640

Offset

1,1

Comments

Column 4 of A223202.

Links

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

Formula

Empirical: a(n) = 144*a(n-1) - 3840*a(n-2) + 24576*a(n-3).

Empirical g.f.: 64*x*(1 - 36*x + 256*x^2) / (1 - 144*x + 3840*x^2 - 24576*x^3). - Colin Barker, Aug 17 2018

Example

Some solutions for n=3:
..0..2..5..2....0..3..5..3....0..3..1..3....0..1..0..2....0..2..4..5
..3..1..3..4....3..4..2..0....3..0..3..0....3..0..3..4....3..4..0..4
..1..3..4..2....1..5..1..2....4..2..0..1....0..3..5..2....1..0..1..0
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: A333583 A183243 A264075 * A281836 A299080 A299843

Adjacent sequences: A223195 A223196 A223197 * A223199 A223200 A223201

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved