cp's OEIS Frontend

A223328 Rolling cube footprints: number of n X 5 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.

%I A223328 #8 Aug 19 2018 09:36:49
%S A223328 81,9261,1059723,121264857,13876429707,1587890407761,181703507374179,
%T A223328 20792470582897209,2379298227030964827,272264906211251105313,
%U A223328 31155480347969275662483,3565145318286297427548489
%N A223328 Rolling cube footprints: number of n X 5 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.
%C A223328 Column 5 of A223331.
%H A223328 R. H. Hardin, <a href="/A223328/b223328.txt">Table of n, a(n) for n = 1..210</a>
%F A223328 Empirical: a(n) = 117*a(n-1) - 294*a(n-2).
%F A223328 Empirical g.f.: 27*x*(3 - 8*x) / (1 - 117*x + 294*x^2). - _Colin Barker_, Aug 19 2018
%e A223328 Some solutions for n=3:
%e A223328 ..0..2..0..2..6....0..4..6..4..0....0..4..5..7..6....0..4..0..2..3
%e A223328 ..0..2..0..2..6....6..2..0..4..0....0..4..6..4..6....6..2..6..2..0
%e A223328 ..0..2..6..4..0....0..2..0..1..3....0..2..0..2..0....0..2..3..2..0
%e A223328 Vertex neighbors:
%e A223328 0 -> 1 2 4
%e A223328 1 -> 0 3 5
%e A223328 2 -> 0 3 6
%e A223328 3 -> 1 2 7
%e A223328 4 -> 0 5 6
%e A223328 5 -> 1 4 7
%e A223328 6 -> 2 4 7
%e A223328 7 -> 3 5 6
%Y A223328 Cf. A223331.
%K A223328 nonn
%O A223328 1,1
%A A223328 _R. H. Hardin_, Mar 19 2013