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%I #4 Mar 18 2013 07:48:06
%S 729,46875,3889953,347696019,31921015497,2960941376139,
%T 275769851453745,25725360515161923,2401334251012194777,
%U 224209069529029889211,20936162679299127225537,1955051227721359130017011
%N Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge
%C Column 7 of A223209
%H R. H. Hardin, <a href="/A223208/b223208.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 117*a(n-1) -614*a(n-2) -193608*a(n-3) +4171896*a(n-4) +11415328*a(n-5) -842180224*a(n-6) +3384845504*a(n-7) +50528534400*a(n-8) -356768428544*a(n-9) -786566761984*a(n-10) +10681051645952*a(n-11) -6785526038528*a(n-12) -118510105321472*a(n-13) +197530250887168*a(n-14) +559297782349824*a(n-15) -1309510355714048*a(n-16) -1087672042455040*a(n-17) +3564507406925824*a(n-18) +719985279238144*a(n-19) -4461650060509184*a(n-20) +91947477762048*a(n-21) +2549613680656384*a(n-22) -206006306996224*a(n-23) -619282299879424*a(n-24) +65421579386880*a(n-25) +47138239152128*a(n-26) -8245531901952*a(n-27) +260919263232*a(n-28)
%e Some solutions for n=3
%e ..0..5..9..5..9..5..7....0..5..0..2..0..1..4....0..5..0..1..6..1..4
%e ..5..0..5..0..5..9..5....5..0..2..0..5..0..1....5..0..1..0..1..4.17
%e ..0..5..0..1..0..5..7....0..5..0..5..0..2..0....0..5..0..1..4.17..4
%e Face neighbors:
%e 0 -> 1 2 5
%e 1 -> 0 4 6
%e 2 -> 0 3 8
%e 3 -> 2 4 16
%e 4 -> 3 1 17
%e 5 -> 0 7 9
%e 6 -> 1 7 10
%e 7 -> 6 5 11
%e 8 -> 2 9 13
%e 9 -> 8 5 14
%e 10 -> 6 12 17
%e 11 -> 7 12 14
%e 12 -> 11 10 19
%e 13 -> 8 15 16
%e 14 -> 9 11 15
%e 15 -> 14 13 19
%e 16 -> 3 13 18
%e 17 -> 4 10 18
%e 18 -> 16 17 19
%e 19 -> 15 18 12
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 18 2013
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