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A223318 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.

%I A223318 #8 Aug 19 2018 07:36:40
%S A223318 625,274625,122039125,54279694625,24143758634125,10739266230499625,
%T A223318 4776881955584279125,2124782217358970404625,945114307570509938324125,
%U A223318 420391815800244320602909625,186992491150169573406883769125
%N A223318 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 A223318 Column 5 of A223321.
%H A223318 R. H. Hardin, <a href="/A223318/b223318.txt">Table of n, a(n) for n = 1..210</a>
%F A223318 Empirical: a(n) = 479*a(n-1) - 15210*a(n-2).
%F A223318 Conjectures from _Colin Barker_, Aug 19 2018: (Start)
%F A223318 G.f.: 125*x*(5 - 198*x) / (1 - 479*x + 15210*x^2).
%F A223318 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 A223318 (End)
%e A223318 Some solutions for n=3:
%e A223318 ..0..6..2..6.10....0..6..2..6..0....0..6.10..6..0....0..6..0..1..3
%e A223318 ..0..6..0..6..2....0..6..0..6..2....0..6..0..2..4....0..6..2..8..2
%e A223318 ..0..1..0..1..3....0..1..2..1..0....0..2..4.10..4....0..1..2..4..8
%e A223318 Vertex neighbors:
%e A223318 0 -> 1 2 5 6 7
%e A223318 1 -> 0 2 3 7 8
%e A223318 2 -> 0 1 4 6 8
%e A223318 3 -> 1 7 8 9 11
%e A223318 4 -> 2 6 8 9 10
%e A223318 5 -> 0 6 7 10 11
%e A223318 6 -> 0 2 4 5 10
%e A223318 7 -> 0 1 3 5 11
%e A223318 8 -> 1 2 3 4 9
%e A223318 9 -> 3 4 8 10 11
%e A223318 10 -> 4 5 6 9 11
%e A223318 11 -> 3 5 7 9 10
%Y A223318 Cf. A223321.
%K A223318 nonn
%O A223318 1,1
%A A223318 _R. H. Hardin_, Mar 19 2013