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Rolling cube footprints: number of n 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
1

%I #6 Dec 18 2015 18:18:30

%S 1,27,3969,3176523,13876429707,330815891296611,43041050285035823937,

%T 30560274879452174084575347,118414345277803156878479453881947,

%U 2503923842303442402830521022775619070739

%N Rolling cube footprints: number of n 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

%C Diagonal of A223331

%H R. H. Hardin, <a href="/A223327/b223327.txt">Table of n, a(n) for n = 1..13</a>

%e Some solutions for n=3

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

%e ..0..2..6....5..1..5....0..4..5....5..4..6....5..4..0....0..1..5....3..1..3

%e ..6..4..5....3..7..3....6..4..5....0..2..6....6..4..6....0..1..5....0..1..3

%e Vertex neighbors:

%e 0 -> 1 2 4

%e 1 -> 0 3 5

%e 2 -> 0 3 6

%e 3 -> 1 2 7

%e 4 -> 0 5 6

%e 5 -> 1 4 7

%e 6 -> 2 4 7

%e 7 -> 3 5 6

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 19 2013