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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
1

%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