%I #7 Aug 19 2018 07:36:46

%S 3125,3570125,4176940625,4903804407125,5759605530667625,

%T 6765094542682458125,7946162712131677450625,9333430848774501484101125,

%U 10962893764533341367143473625,12876834103685350223700565272125

%N 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 Column 6 of A223321.

%H R. H. Hardin, <a href="/A223319/b223319.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1366*a(n-1) - 232713*a(n-2) + 9253764*a(n-3).

%F 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 Some solutions for n=3:

%e ..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 ..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 ..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 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