cp's OEIS Frontend

A223270 Rolling cube footprints: number of 2 X n 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 A223270 #7 Aug 18 2018 08:42:58
%S A223270 6,48,576,6144,67584,737280,8060928,88080384,962592768,10519314432,
%T A223270 114957484032,1256277934080,13728862961664,150031797583872,
%U A223270 1639577995444224,17917641486237696,195807627744116736
%N A223270 Rolling cube footprints: number of 2 X n 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 A223270 Row 2 of A223269.
%H A223270 R. H. Hardin, <a href="/A223270/b223270.txt">Table of n, a(n) for n = 1..210</a>
%F A223270 Empirical: a(n) = 8*a(n-1) + 32*a(n-2).
%F A223270 Conjectures from _Colin Barker_, Aug 18 2018: (Start)
%F A223270 G.f.: 6*x / (1 - 8*x - 32*x^2).
%F A223270 a(n) = (sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n)) / 4.
%F A223270 (End)
%e A223270 Some solutions for n=3:
%e A223270 ..0..2..0....0..2..1....0..3..4....0..2..4....0..2..0....0..1..2....0..4..2
%e A223270 ..5..3..4....4..3..1....4..2..4....1..3..1....1..3..5....2..4..3....0..1..0
%e A223270 Face neighbors:
%e A223270 0.->.1.2.3.4
%e A223270 1.->.0.2.3.5
%e A223270 2.->.0.1.4.5
%e A223270 3.->.0.1.4.5
%e A223270 4.->.0.3.2.5
%e A223270 5.->.1.3.4.2
%Y A223270 Cf. A223269.
%K A223270 nonn
%O A223270 1,1
%A A223270 _R. H. Hardin_, Mar 19 2013