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A223235 Rolling icosahedron footprints: number of 3 X n 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 A223235 #7 Aug 17 2018 09:23:04
%S A223235 144,845,25225,492365,11043445,236027705,5127809545,110781320885,
%T A223235 2397904326205,51869658014705,1122255717889585,24279356422739885,
%U A223235 525283571663978725,11364402460546714985,245867265513538637785
%N A223235 Rolling icosahedron footprints: number of 3 X n 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 A223235 Row 3 of A223233.
%H A223235 R. H. Hardin, <a href="/A223235/b223235.txt">Table of n, a(n) for n = 1..210</a>
%F A223235 Empirical: a(n) = 18*a(n-1) + 103*a(n-2) - 552*a(n-3) + 540*a(n-4) for n>5.
%F A223235 Empirical g.f.: x*(144 - 1747*x - 4817*x^2 + 30768*x^3 - 28620*x^4) / (1 - 18*x - 103*x^2 + 552*x^3 - 540*x^4). - _Colin Barker_, Aug 17 2018
%e A223235 Some solutions for n=3:
%e A223235 ..0..2..0....0..5..7....0..6..2....0..2..1....0..6..0....0..1..7....0..1..7
%e A223235 ..0..5..0....0..5..6....0..6..5....1..2..6....0..6..0....0..1..3....0..1..8
%e A223235 .11..5..0....0..5..6....5..7..0....4..2..1....4..2..0....3..7..0....7..1..8
%e A223235 Vertex neighbors:
%e A223235 0 -> 1 2 5 6 7
%e A223235 1 -> 0 2 3 7 8
%e A223235 2 -> 0 1 4 6 8
%e A223235 3 -> 1 7 8 9 11
%e A223235 4 -> 2 6 8 9 10
%e A223235 5 -> 0 6 7 10 11
%e A223235 6 -> 0 2 4 5 10
%e A223235 7 -> 0 1 3 5 11
%e A223235 8 -> 1 2 3 4 9
%e A223235 9 -> 3 4 8 10 11
%e A223235 10 -> 4 5 6 9 11
%e A223235 11 -> 3 5 7 9 10
%Y A223235 Cf. A223233.
%K A223235 nonn
%O A223235 1,1
%A A223235 _R. H. Hardin_, Mar 18 2013