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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. 1
6, 48, 576, 6144, 67584, 737280, 8060928, 88080384, 962592768, 10519314432, 114957484032, 1256277934080, 13728862961664, 150031797583872, 1639577995444224, 17917641486237696, 195807627744116736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A223269.

LINKS

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

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)

EXAMPLE

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

CROSSREFS

Cf. A223269.

Sequence in context: A002170 A153467 A209670 * A052731 A052711 A113388

Adjacent sequences:  A223267 A223268 A223269 * A223271 A223272 A223273

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved

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Last modified February 21 15:31 EST 2019. Contains 320374 sequences. (Running on oeis4.)