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A223335 Rolling cube footprints: number of 6 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 A223335 #6 Apr 16 2024 22:43:27
%S A223335 32768,177147,36756909,7626831723,1587890407761,330815891296611,
%T A223335 68935627430614161,14365712340521444763,2993767914167348634225,
%U A223335 623894511848537009674251,130018376961215856234304281
%N A223335 Rolling cube footprints: number of 6 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 A223335 Row 6 of A223331.
%H A223335 R. H. Hardin, <a href="/A223335/b223335.txt">Table of n, a(n) for n = 1..210</a>
%F A223335 Empirical: a(n) = 363*a(n-1) -42090*a(n-2) +2394790*a(n-3) -76949379*a(n-4) +1439989707*a(n-5) -14188685367*a(n-6) +22105928025*a(n-7) +1145452404696*a(n-8) -13381549738272*a(n-9) +56254263011793*a(n-10) +62916731731323*a(n-11) -1574353040753800*a(n-12) +5560131978318054*a(n-13) -1833699655619436*a(n-14) -34189681765260294*a(n-15) +75258675804889728*a(n-16) -6463571598539280*a(n-17) -143095150109785392*a(n-18) +141900806436429312*a(n-19) -28670292192657024*a(n-20) for n>25.
%e A223335 Some solutions for n=3
%e A223335 ..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
%e A223335 ..0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0....0..4..0
%e A223335 ..0..2..6....0..2..6....0..4..0....0..4..6....0..2..6....0..4..6....0..2..0
%e A223335 ..6..4..0....3..7..5....0..2..0....6..4..0....6..7..5....6..2..6....6..2..0
%e A223335 ..0..1..0....3..1..0....0..1..3....6..2..0....5..4..0....3..2..6....6..2..6
%e A223335 ..5..4..5....0..2..0....0..2..0....6..4..6....0..2..3....0..2..6....0..4..0
%e A223335 Vertex neighbors:
%e A223335 0 -> 1 2 4
%e A223335 1 -> 0 3 5
%e A223335 2 -> 0 3 6
%e A223335 3 -> 1 2 7
%e A223335 4 -> 0 5 6
%e A223335 5 -> 1 4 7
%e A223335 6 -> 2 4 7
%e A223335 7 -> 3 5 6
%Y A223335 Cf. A223331.
%K A223335 nonn
%O A223335 1,1
%A A223335 _R. H. Hardin_, Mar 19 2013