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A223200 Rolling cube footprints: number of nX6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.

%I A223200 #6 Jul 23 2025 03:51:05
%S A223200 1024,995328,1020002304,1061444124672,1110327429169152,
%T A223200 1163614255186968576,1220273386789986631680,1280001086812985197854720,
%U A223200 1342770055307877057357152256,1408661948573682047511982768128
%N A223200 Rolling cube footprints: number of nX6 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.
%C A223200 Column 6 of A223202
%H A223200 R. H. Hardin, <a href="/A223200/b223200.txt">Table of n, a(n) for n = 1..210</a>
%F A223200 Empirical: a(n) = 1920*a(n-1) -1191936*a(n-2) +335020032*a(n-3) -48670703616*a(n-4) +3778497478656*a(n-5) -147884313935872*a(n-6) +2269391999729664*a(n-7)
%e A223200 Some solutions for n=3
%e A223200 ..0..3..0..4..2..4....0..3..0..3..0..2....0..3..0..3..1..0....0..3..0..2..5..1
%e A223200 ..3..0..3..5..1..5....3..0..3..5..2..1....3..0..3..0..3..4....3..0..3..0..1..0
%e A223200 ..0..3..1..2..0..3....0..3..0..3..0..3....0..3..4..3..5..3....0..3..0..3..5..2
%e A223200 Face neighbors:
%e A223200 0,5 -> 1 2 3 4
%e A223200 1,4 -> 0 2 3 5
%e A223200 2,3 -> 0 1 4 5
%K A223200 nonn
%O A223200 1,1
%A A223200 _R. H. Hardin_ Mar 18 2013