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%I #8 Aug 19 2018 09:36:57
%S 243,64827,17324685,4630596579,1237689159021,330815891296611,
%T 88422165323034669,23633929115222765283,6316997592145707860589,
%U 1688439462802532886238947,451294745322310558858483245
%N Rolling cube footprints: number of n X 6 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 Column 6 of A223331.
%H R. H. Hardin, <a href="/A223329/b223329.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 282*a(n-1) - 3969*a(n-2) + 9604*a(n-3).
%F Empirical g.f.: 27*x*(9 - 137*x + 294*x^2) / (1 - 282*x + 3969*x^2 - 9604*x^3). - _Colin Barker_, Aug 19 2018
%e Some solutions for n=3:
%e ..0..4..0..4..6..2....0..4..0..1..0..1....0..4..6..7..5..1....0..4..0..1..5..4
%e ..0..4..0..2..0..2....0..4..5..4..5..4....0..4..5..4..0..1....0..4..5..4..6..7
%e ..0..4..6..4..0..2....0..4..5..4..5..4....0..4..5..4..0..2....0..4..5..4..5..7
%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
%Y Cf. A223331.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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