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A223268 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.

%I A223268 #6 Jul 23 2025 03:56:31
%S A223268 4096,8060928,19084083200,47175115472896,118579442837618688,
%T A223268 300099634959879241728,761838097494483172065280,
%U A223268 1936846409617575899985608704,4927624374993058505713514446848
%N A223268 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, diagonal or antidiagonal neighbor moves across a corresponding cube edge.
%C A223268 Column 7 of A223269
%H A223268 R. H. Hardin, <a href="/A223268/b223268.txt">Table of n, a(n) for n = 1..210</a>
%F A223268 Empirical: a(n) = 5248*a(n-1) -8994816*a(n-2) +5490343936*a(n-3) +187904819200*a(n-4) -1264610170634240*a(n-5) +256551247132229632*a(n-6) +70752113095943913472*a(n-7) -23366404249055043518464*a(n-8) -533913337097412407197696*a(n-9) +674953674297109781457928192*a(n-10) -40751378221934631192876810240*a(n-11) -5757910579286783501424165650432*a(n-12) +721053031162241165678293693759488*a(n-13) -13066308561852474555927268289413120*a(n-14) -1348009507077897319716382214971195392*a(n-15) +58039494284702303231713887968022233088*a(n-16) -3987683987354747618711421180841033728*a(n-17) -29604565922121646321313590846563834396672*a(n-18) +348449143727040986586495598010130648530944*a(n-19)
%e A223268 Some solutions for n=3
%e A223268 ..0..3..0..3..0..2..0....0..3..0..3..4..3..4....0..3..0..3..1..2..4
%e A223268 ..0..3..0..3..5..4..5....0..3..0..3..5..2..5....0..3..0..3..0..2..5
%e A223268 ..0..3..0..4..5..4..2....0..3..0..1..0..2..1....0..3..0..3..1..2..1
%e A223268 Face neighbors:
%e A223268 0.->.1.2.3.4
%e A223268 1.->.0.2.3.5
%e A223268 2.->.0.1.4.5
%e A223268 3.->.0.1.4.5
%e A223268 4.->.0.3.2.5
%e A223268 5.->.1.3.4.2
%K A223268 nonn
%O A223268 1,1
%A A223268 _R. H. Hardin_ Mar 19 2013