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A223272 Rolling cube footprints: number of 4Xn 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 A223272 #6 Jul 23 2025 03:56:45
%S A223272 216,6912,765952,63438848,5889851392,522106961920,47175115472896,
%T A223272 4228713130491904,380326363447427072,34157975785279848448,
%U A223272 3069635685131267080192,275785779148632316968960
%N A223272 Rolling cube footprints: number of 4Xn 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 A223272 Row 4 of A223269
%H A223272 R. H. Hardin, <a href="/A223272/b223272.txt">Table of n, a(n) for n = 1..210</a>
%F A223272 Empirical: a(n) = 48*a(n-1) +4096*a(n-2) -12288*a(n-3) -1638400*a(n-4) +2097152*a(n-5) +67108864*a(n-6) for n>7
%e A223272 Some solutions for n=3
%e A223272 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..1....0..3..1....0..3..0
%e A223272 ..0..2..1....4..2..5....0..4..0....5..4..0....1..3..4....4..2..4....5..2..0
%e A223272 ..4..2..5....1..3..5....5..3..5....2..4..5....1..3..5....4..3..5....1..3..5
%e A223272 ..4..2..4....5..2..5....5..3..5....2..4..2....5..2..0....4..2..4....4..3..4
%e A223272 Face neighbors:
%e A223272 0.->.1.2.3.4
%e A223272 1.->.0.2.3.5
%e A223272 2.->.0.1.4.5
%e A223272 3.->.0.1.4.5
%e A223272 4.->.0.3.2.5
%e A223272 5.->.1.3.4.2
%K A223272 nonn
%O A223272 1,1
%A A223272 _R. H. Hardin_ Mar 19 2013