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A223271 Rolling cube footprints: number of 3 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 A223271 #7 Aug 18 2018 08:42:52
%S A223271 36,576,20992,622592,19726336,611319808,19084083200,594316099584,
%T A223271 18523120205824,577157705236480,17985124012392448,560427673747193856,
%U A223271 17463446426942963712,544175431737222889472,16956974709073621549056
%N A223271 Rolling cube footprints: number of 3 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 A223271 Row 3 of A223269.
%H A223271 R. H. Hardin, <a href="/A223271/b223271.txt">Table of n, a(n) for n = 1..210</a>
%F A223271 Empirical: a(n) = 24*a(n-1) + 256*a(n-2) - 1024*a(n-3) for n>4.
%F A223271 Empirical g.f.: 4*x*(9 - 72*x - 512*x^2 + 2048*x^3) / (1 - 24*x - 256*x^2 + 1024*x^3). - _Colin Barker_, Aug 18 2018
%e A223271 Some solutions for n=3:
%e A223271 ..0..2..5....0..2..1....0..1..0....0..1..0....0..1..5....0..2..0....0..1..5
%e A223271 ..0..2..0....4..3..1....0..3..0....5..3..5....0..1..0....5..1..0....0..3..5
%e A223271 ..4..3..4....0..2..1....0..4..5....4..2..0....2..4..3....0..3..5....5..3..1
%e A223271 Face neighbors:
%e A223271 0.->.1.2.3.4
%e A223271 1.->.0.2.3.5
%e A223271 2.->.0.1.4.5
%e A223271 3.->.0.1.4.5
%e A223271 4.->.0.3.2.5
%e A223271 5.->.1.3.4.2
%Y A223271 Cf. A223269.
%K A223271 nonn
%O A223271 1,1
%A A223271 _R. H. Hardin_, Mar 19 2013