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A223229 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

%I A223229 #7 Aug 17 2018 09:22:36
%S A223229 125,7445,492365,32837285,2191464605,146259564725,9761484584045,
%T A223229 651489782832965,43480983274973885,2901957882023749205,
%U A223229 193679142376194109325,12926311034495639900645,862713015509641940473565
%N A223229 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.
%C A223229 Column 4 of A223233.
%H A223229 R. H. Hardin, <a href="/A223229/b223229.txt">Table of n, a(n) for n = 1..210</a>
%F A223229 Empirical: a(n) = 73*a(n-1) - 423*a(n-2) + 351*a(n-3).
%F A223229 Empirical g.f.: 5*x*(25 - 336*x + 351*x^2) / ((1 - x)*(1 - 72*x + 351*x^2)). - _Colin Barker_, Aug 17 2018
%e A223229 Some solutions for n=3:
%e A223229 ..0..6.10..5....0..5..7..0....0..5..0..7....0..1..7..5....0..2..4..2
%e A223229 ..0..6.10..6....0..5..7..3....6..5..0..6....0..1..7..5....6..2..8..9
%e A223229 ..0..6..5..6....0..5..7..3....0..2..0..5....3..1..7..0....0..2..8..1
%e A223229 Vertex neighbors:
%e A223229 0 -> 1 2 5 6 7
%e A223229 1 -> 0 2 3 7 8
%e A223229 2 -> 0 1 4 6 8
%e A223229 3 -> 1 7 8 9 11
%e A223229 4 -> 2 6 8 9 10
%e A223229 5 -> 0 6 7 10 11
%e A223229 6 -> 0 2 4 5 10
%e A223229 7 -> 0 1 3 5 11
%e A223229 8 -> 1 2 3 4 9
%e A223229 9 -> 3 4 8 10 11
%e A223229 10 -> 4 5 6 9 11
%e A223229 11 -> 3 5 7 9 10
%Y A223229 Cf. A223233.
%K A223229 nonn
%O A223229 1,1
%A A223229 _R. H. Hardin_, Mar 18 2013