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%I #7 Aug 18 2018 08:42:52
%S 36,576,20992,622592,19726336,611319808,19084083200,594316099584,
%T 18523120205824,577157705236480,17985124012392448,560427673747193856,
%U 17463446426942963712,544175431737222889472,16956974709073621549056
%N 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.
%C Row 3 of A223269.
%H R. H. Hardin, <a href="/A223271/b223271.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 24*a(n-1) + 256*a(n-2) - 1024*a(n-3) for n>4.
%F 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
%e Some solutions for n=3:
%e ..0..2..5....0..2..1....0..1..0....0..1..0....0..1..5....0..2..0....0..1..5
%e ..0..2..0....4..3..1....0..3..0....5..3..5....0..1..0....5..1..0....0..3..5
%e ..4..3..4....0..2..1....0..4..5....4..2..0....2..4..3....0..3..5....5..3..1
%e Face neighbors:
%e 0.->.1.2.3.4
%e 1.->.0.2.3.5
%e 2.->.0.1.4.5
%e 3.->.0.1.4.5
%e 4.->.0.3.2.5
%e 5.->.1.3.4.2
%Y Cf. A223269.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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