cp's OEIS Frontend

A223334 Rolling cube footprints: number of 5Xn 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 A223334 #6 Jul 23 2025 04:01:11
%S A223334 4096,19683,1750329,155649627,13876429707,1237689159021,
%T A223334 110409049892673,9849460912651899,878665830242295627,
%U A223334 78385506226393458141,6992749153173468569913,623821244550672567090699
%N A223334 Rolling cube footprints: number of 5Xn 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 A223334 Row 5 of A223331
%H A223334 R. H. Hardin, <a href="/A223334/b223334.txt">Table of n, a(n) for n = 1..210</a>
%F A223334 Empirical: a(n) = 131*a(n-1) -4376*a(n-2) +62456*a(n-3) -430316*a(n-4) +1335338*a(n-5) -688543*a(n-6) -5374827*a(n-7) +10631682*a(n-8) -5437152*a(n-9) for n>13
%e A223334 Some solutions for n=3
%e A223334 ..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
%e A223334 ..0..4..6....0..2..6....6..4..6....0..4..5....0..4..6....0..2..3....0..4..0
%e A223334 ..0..4..0....3..2..0....6..7..5....5..4..6....5..4..5....3..7..3....6..2..3
%e A223334 ..0..4..5....0..2..3....6..4..0....6..7..5....5..1..0....3..1..0....6..2..0
%e A223334 ..6..4..5....6..7..3....0..2..6....5..1..5....3..2..6....3..1..3....6..2..0
%e A223334 Vertex neighbors:
%e A223334 0 -> 1 2 4
%e A223334 1 -> 0 3 5
%e A223334 2 -> 0 3 6
%e A223334 3 -> 1 2 7
%e A223334 4 -> 0 5 6
%e A223334 5 -> 1 4 7
%e A223334 6 -> 2 4 7
%e A223334 7 -> 3 5 6
%K A223334 nonn
%O A223334 1,1
%A A223334 _R. H. Hardin_ Mar 19 2013