A223265 - OEIS

A223265

Rolling cube footprints: number of n X 4 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 #7 Aug 18 2018 08:43:04

%S 64,6144,622592,63438848,6467616768,659411697664,67231270567936,

%T 6854664725200896,698877628160933888,71255117675418877952,

%U 7264922488410118029312,740706078202304288260096

%N Rolling cube footprints: number of n X 4 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 Column 4 of A223269.

%H R. H. Hardin, <a href="/A223265/b223265.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 112*a(n-1) - 1024*a(n-2).

%F Empirical g.f.: 64*x*(1 - 16*x) / (1 - 112*x + 1024*x^2). - _Colin Barker_, Aug 18 2018

%e Some solutions for n=3:

%e ..0..3..5..1....0..4..2..0....0..3..0..1....0..3..5..2....0..3..4..3

%e ..0..3..5..2....0..4..2..0....0..1..0..3....0..2..0..3....0..2..0..2

%e ..0..2..1..2....0..4..3..4....0..1..0..4....0..3..5..3....1..2..1..2

%e Face neighbors:

%e 0.->.1.2.3.4

%e 1.->.0.2.3.5

%e 2.->.0.1.4.5

%e 3.->.0.1.4.5

%e 4.->.0.3.2.5

%e 5.->.1.3.4.2

%Y Cf. A223269.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013