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%I #9 Aug 18 2018 08:43:12
%S 25,845,28885,988625,33841585,1158447605,39655444525,1357467150905,
%T 46468199390665,1590678314378525,54451378224988165,
%U 1863954869994720545,63806057268775907425,2184179997984165531845,74767858535726198152285
%N Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or vertical neighbor moves along an icosahedral edge.
%C Column 3 of A223263.
%H R. H. Hardin, <a href="/A223258/b223258.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 38*a(n-1) - 129*a(n-2).
%F Conjectures from _Colin Barker_, Aug 18 2018: (Start)
%F G.f.: 5*x*(5 - 21*x) / (1 - 38*x + 129*x^2).
%F a(n) = (5*((19-2*sqrt(58))^n*(-41+7*sqrt(58)) + (19+2*sqrt(58))^n*(41+7*sqrt(58)))) / (86*sqrt(58)).
%F (End)
%e Some solutions for n=3:
%e ..0..1..3....0..6..2....0..5..6....0..1..8....0..7..1....0..7..1....0..2..8
%e ..6..2..8....5.10..6....5.10..5....1..0..2....6..5..0....7..1..3....1..8..4
%e ..2..0..2...10..6..2....7..5..7....7..5..0....2..0..1....5..7.11....8..4..8
%e Vertex neighbors:
%e 0.->.1.2.5.6.7
%e 1.->.0.2.3.7.8
%e 2.->.0.1.4.6.8
%e 3.->.1.7.8.9.11
%e 4.->.2.6.8.9.10
%e 5.->.0.6.7.10.11
%e 6.->.0.2.4.5.10
%e 7.->.0.1.3.5.11
%e 8.->.1.2.3.4.9
%e 9.->.3.4.8.10.11
%e 10.->.4.5.6.9.11
%e 11.->.3.5.7.9.10
%Y Cf. A223263.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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