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A223267 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.

%I A223267 #6 Jul 23 2025 03:56:24
%S A223267 1024,737280,611319808,522106961920,450204914417664,
%T A223267 389343801904201728,337035427916688654336,291846966499723716853760,
%U A223267 252743669925904582659014656,218887233158696603085046808576
%N A223267 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 A223267 Column 6 of A223269
%H A223267 R. H. Hardin, <a href="/A223267/b223267.txt">Table of n, a(n) for n = 1..210</a>
%F A223267 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 A223267 Some solutions for n=3
%e A223267 ..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 A223267 ..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 A223267 ..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 A223267 Face neighbors:
%e A223267 0.->.1.2.3.4
%e A223267 1.->.0.2.3.5
%e A223267 2.->.0.1.4.5
%e A223267 3.->.0.1.4.5
%e A223267 4.->.0.3.2.5
%e A223267 5.->.1.3.4.2
%K A223267 nonn
%O A223267 1,1
%A A223267 _R. H. Hardin_ Mar 19 2013