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A223274 Rolling cube footprints: number of 6Xn 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 A223274 #6 Jul 23 2025 03:56:58
%S A223274 7776,995328,1020002304,659411697664,534392715870208,
%T A223274 389343801904201728,300099634959879241728,224781443200799995854848,
%U A223274 170981358780674940558376960,129013576934490162920595390464
%N A223274 Rolling cube footprints: number of 6Xn 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 A223274 Row 6 of A223269
%H A223274 R. H. Hardin, <a href="/A223274/b223274.txt">Table of n, a(n) for n = 1..210</a>
%F A223274 Empirical: a(n) = 384*a(n-1) +446464*a(n-2) -67108864*a(n-3) -52881784832*a(n-4) +4312147165184*a(n-5) +2494998041853952*a(n-6) -172245093560877056*a(n-7) -56567744594563825664*a(n-8) +4056230054786020409344*a(n-9) +644319406221573287313408*a(n-10) -49152677749972407368548352*a(n-11) -3878710988338500226623995904*a(n-12) +310939347582341467621952585728*a(n-13) +12871152730646806229128124039168*a(n-14) -1063719785796591567291470875459584*a(n-15) -23908207232954463569578196629192704*a(n-16) +1970557787452381691709019145944170496*a(n-17) +24560537696530709963129597105272782848*a(n-18) -1895084507428041387861060550238750638080*a(n-19) -13078274250527787273500557666098310283264*a(n-20) +864147070795723227965239815572975372992512*a(n-21) +2646035685177217491891200947389429612281856*a(n-22) -146348640365357214366328151164254872382996480*a(n-23) for n>24
%e A223274 Some solutions for n=3
%e A223274 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
%e A223274 ..0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0....0..3..0
%e A223274 ..0..3..1....0..3..1....0..3..4....0..3..0....0..3..0....0..3..0....0..3..0
%e A223274 ..1..2..4....4..3..0....0..3..1....0..2..5....1..3..5....4..2..4....4..3..1
%e A223274 ..0..2..4....0..2..0....5..3..5....0..4..5....0..3..0....4..2..4....0..3..4
%e A223274 ..4..3..5....0..4..0....1..2..5....5..2..0....5..1..5....5..2..5....0..3..0
%e A223274 Face neighbors:
%e A223274 0.->.1.2.3.4
%e A223274 1.->.0.2.3.5
%e A223274 2.->.0.1.4.5
%e A223274 3.->.0.1.4.5
%e A223274 4.->.0.3.2.5
%e A223274 5.->.1.3.4.2
%K A223274 nonn
%O A223274 1,1
%A A223274 _R. H. Hardin_ Mar 19 2013