cp's OEIS Frontend

A223333 Rolling cube footprints: number of 4 X n 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 A223333 #10 Aug 19 2018 16:42:31
%S A223333 512,2187,83349,3176523,121264857,4630596579,176834343105,
%T A223333 6753068175483,257891143282857,9848539671395859,376103406869296785,
%U A223333 14362918587487614123,548501892736263190137,20946601106278812695619
%N A223333 Rolling cube footprints: number of 4 X n 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.
%H A223333 R. H. Hardin, <a href="/A223333/b223333.txt">Table of n, a(n) for n = 1..210</a>
%F A223333 Empirical: a(n) = 48*a(n-1) - 402*a(n-2) + 1064*a(n-3) - 789*a(n-4) for n>7.
%F A223333 Empirical g.f.: x*(512 - 22389*x + 184197*x^2 - 489823*x^3 + 375051*x^4 - 112104*x^5 + 121716*x^6) / ((1 - 3*x)*(1 - 45*x + 267*x^2 - 263*x^3)). - _Colin Barker_, Aug 19 2018
%e A223333 Some solutions for n=3:
%e A223333 ..0..2..0....0..1..0....0..2..3....0..1..0....0..1..3....0..4..5....0..1..0
%e A223333 ..6..2..3....0..1..0....6..7..3....0..2..0....3..1..0....5..4..5....5..4..5
%e A223333 ..6..7..5....0..1..3....3..7..6....3..1..3....5..1..0....0..1..0....0..1..0
%e A223333 ..3..1..3....5..1..0....6..2..6....0..1..0....3..1..5....3..2..6....0..4..5
%e A223333 Vertex neighbors:
%e A223333 0 -> 1 2 4
%e A223333 1 -> 0 3 5
%e A223333 2 -> 0 3 6
%e A223333 3 -> 1 2 7
%e A223333 4 -> 0 5 6
%e A223333 5 -> 1 4 7
%e A223333 6 -> 2 4 7
%e A223333 7 -> 3 5 6
%Y A223333 Row 4 of A223331.
%K A223333 nonn
%O A223333 1,1
%A A223333 _R. H. Hardin_, Mar 19 2013