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%I #8 Aug 19 2018 07:36:40
%S 625,274625,122039125,54279694625,24143758634125,10739266230499625,
%T 4776881955584279125,2124782217358970404625,945114307570509938324125,
%U 420391815800244320602909625,186992491150169573406883769125
%N Rolling icosahedron footprints: number of n X 5 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.
%C Column 5 of A223321.
%H R. H. Hardin, <a href="/A223318/b223318.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 479*a(n-1) - 15210*a(n-2).
%F Conjectures from _Colin Barker_, Aug 19 2018: (Start)
%F G.f.: 125*x*(5 - 198*x) / (1 - 479*x + 15210*x^2).
%F a(n) = (25*2^(-1-n)*((479-sqrt(168601))^n*(-3181+11*sqrt(168601)) + (479+sqrt(168601))^n*(3181+11*sqrt(168601)))) / (169*sqrt(168601)).
%F (End)
%e Some solutions for n=3:
%e ..0..6..2..6.10....0..6..2..6..0....0..6.10..6..0....0..6..0..1..3
%e ..0..6..0..6..2....0..6..0..6..2....0..6..0..2..4....0..6..2..8..2
%e ..0..1..0..1..3....0..1..2..1..0....0..2..4.10..4....0..1..2..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. A223321.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013
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