cp's OEIS Frontend

A223201 Rolling cube footprints: number of nX7 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.

%I A223201 #6 Jul 23 2025 03:51:11
%S A223201 4096,11943936,37222350848,118404195287040,379529320596504576,
%T A223201 1220273386789986631680,3928452022261522225954816,
%U A223201 12653687328474521535529353216,40767113911221149476183875780608
%N A223201 Rolling cube footprints: number of nX7 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 A223201 Column 7 of A223202
%H A223201 R. H. Hardin, <a href="/A223201/b223201.txt">Table of n, a(n) for n = 1..210</a>
%F A223201 Empirical: a(n) = 7040*a(n-1) -18169856*a(n-2) +23760732160*a(n-3) -18040473255936*a(n-4) +8500736711196672*a(n-5) -2561598209927413760*a(n-6) +496452053123372941312*a(n-7) -61015776557932010799104*a(n-8) +4604307320797904083353600*a(n-9) -203533995411681708710297600*a(n-10) +5009788596483023299982393344*a(n-11) -63134942003554394019855335424*a(n-12) +316912650057057350374175801344*a(n-13)
%e A223201 Some solutions for n=3
%e A223201 ..0..3..0..3..1..3..5....0..3..0..3..0..3..1....0..3..0..3..0..2..0
%e A223201 ..3..0..3..0..2..0..2....3..0..3..0..3..0..2....3..0..3..0..3..5..1
%e A223201 ..0..3..0..3..4..3..0....0..3..0..3..0..3..5....0..3..0..4..0..1..0
%e A223201 Face neighbors:
%e A223201 0,5 -> 1 2 3 4
%e A223201 1,4 -> 0 2 3 5
%e A223201 2,3 -> 0 1 4 5
%K A223201 nonn
%O A223201 1,1
%A A223201 _R. H. Hardin_ Mar 18 2013