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%I #8 Aug 17 2018 09:22:00
%S 64,6912,765952,85327872,9515827200,1061444124672,118404195287040,
%T 13208119651860480,1473383170773614592,164357898631630553088,
%U 18334348775748242767872,2045221757767217986928640
%N 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.
%C Column 4 of A223202.
%H R. H. Hardin, <a href="/A223198/b223198.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 144*a(n-1) - 3840*a(n-2) + 24576*a(n-3).
%F 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
%e Some solutions for n=3:
%e ..0..2..5..2....0..3..5..3....0..3..1..3....0..1..0..2....0..2..4..5
%e ..3..1..3..4....3..4..2..0....3..0..3..0....3..0..3..4....3..4..0..4
%e ..1..3..4..2....1..5..1..2....4..2..0..1....0..3..5..2....1..0..1..0
%e Face neighbors:
%e 0,5 -> 1 2 3 4
%e 1,4 -> 0 2 3 5
%e 2,3 -> 0 1 4 5
%Y Cf. A223202.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 18 2013
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