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A223319 Rolling icosahedron footprints: number of n X 6 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 A223319 #7 Aug 19 2018 07:36:46
%S A223319 3125,3570125,4176940625,4903804407125,5759605530667625,
%T A223319 6765094542682458125,7946162712131677450625,9333430848774501484101125,
%U A223319 10962893764533341367143473625,12876834103685350223700565272125
%N A223319 Rolling icosahedron footprints: number of n X 6 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 A223319 Column 6 of A223321.
%H A223319 R. H. Hardin, <a href="/A223319/b223319.txt">Table of n, a(n) for n = 1..210</a>
%F A223319 Empirical: a(n) = 1366*a(n-1) - 232713*a(n-2) + 9253764*a(n-3).
%F A223319 Empirical g.f.: 125*x*(25 - 5589*x + 219024*x^2) / (1 - 1366*x + 232713*x^2 - 9253764*x^3). - _Colin Barker_, Aug 19 2018
%e A223319 Some solutions for n=3:
%e A223319 ..0..6..0..6..0..5....0..6..0..1..8..2....0..6..0..6..0..2....0..6..0..6..0..2
%e A223319 ..0..6..0..5..6..4....0..6..0..2..0..6....0..6..0..1..8..3....0..6..0..5..0..7
%e A223319 ..0..1..7..5.10.11....0..1..0..2..4..8....0..1..3..9..8..3....0..1..7..1..3..7
%e A223319 Vertex neighbors:
%e A223319 0 -> 1 2 5 6 7
%e A223319 1 -> 0 2 3 7 8
%e A223319 2 -> 0 1 4 6 8
%e A223319 3 -> 1 7 8 9 11
%e A223319 4 -> 2 6 8 9 10
%e A223319 5 -> 0 6 7 10 11
%e A223319 6 -> 0 2 4 5 10
%e A223319 7 -> 0 1 3 5 11
%e A223319 8 -> 1 2 3 4 9
%e A223319 9 -> 3 4 8 10 11
%e A223319 10 -> 4 5 6 9 11
%e A223319 11 -> 3 5 7 9 10
%Y A223319 Cf. A223321.
%K A223319 nonn
%O A223319 1,1
%A A223319 _R. H. Hardin_, Mar 19 2013