%I #4 Mar 19 2013 07:23:33
%S 1024,737280,611319808,522106961920,450204914417664,
%T 389343801904201728,337035427916688654336,291846966499723716853760,
%U 252743669925904582659014656,218887233158696603085046808576
%N Rolling cube footprints: number of nX6 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 Column 6 of A223269
%H R. H. Hardin, <a href="/A223267/b223267.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 1152*a(n-1) -229376*a(n-2) -21233664*a(n-3) +4697620480*a(n-4) +12884901888*a(n-5) -17798344474624*a(n-6) +343047627866112*a(n-7) +6755399441055744*a(n-8) -90071992547409920*a(n-9)
%e Some solutions for n=3
%e ..0..3..0..2..1..3....0..3..0..2..4..2....0..3..0..2..0..2....0..3..0..2..1..3
%e ..0..3..0..2..0..2....0..3..0..2..4..2....0..3..0..1..5..1....0..3..0..3..0..2
%e ..0..3..0..4..5..1....0..3..0..3..1..3....0..3..0..4..3..4....0..3..0..2..5..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
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 19 2013