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A223478 Rolling icosahedron face footprints: number of n X 6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

%I A223478 #8 Aug 20 2018 14:37:05
%S A223478 243,16875,1296675,101331675,7939566675,622332801675,48783753036675,
%T A223478 3824122400271675,299770559674506675,23498831496975741675,
%U A223478 1842059141815703976675,144397899075877259211675
%N A223478 Rolling icosahedron face footprints: number of n X 6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.
%C A223478 Column 6 of A223480.
%H A223478 R. H. Hardin, <a href="/A223478/b223478.txt">Table of n, a(n) for n = 1..210</a>
%F A223478 Empirical: a(n) = 101*a(n-1) -1900*a(n-2) +10000*a(n-3).
%F A223478 Empirical g.f.: 27*x*(9 - 284*x + 2000*x^2) / (1 - 101*x + 1900*x^2 - 10000*x^3). - _Colin Barker_, Aug 20 2018
%e A223478 Some solutions for n=3:
%e A223478 ..0..1..6..1..4..3....0..1..4..1..4..1....0..1..0..5..9..8....0..1..0..2..3.16
%e A223478 ..0..1..0..1..4..1....0..1..4..1..4..3....0..5..9..5..9..5....0..2..0..2..3.16
%e A223478 ..0..1..4..1..6..1....6..1..4..3..2..0....0..5..9.14..9.14....0..2..3..4..3..4
%e A223478 Face neighbors:
%e A223478 0 -> 1 2 5
%e A223478 1 -> 0 4 6
%e A223478 2 -> 0 3 8
%e A223478 3 -> 2 4 16
%e A223478 4 -> 3 1 17
%e A223478 5 -> 0 7 9
%e A223478 6 -> 1 7 10
%e A223478 7 -> 6 5 11
%e A223478 8 -> 2 9 13
%e A223478 9 -> 8 5 14
%e A223478 10 -> 6 12 17
%e A223478 11 -> 7 12 14
%e A223478 12 -> 11 10 19
%e A223478 13 -> 8 15 16
%e A223478 14 -> 9 11 15
%e A223478 15 -> 14 13 19
%e A223478 16 -> 3 13 18
%e A223478 17 -> 4 10 18
%e A223478 18 -> 16 17 19
%e A223478 19 -> 15 18 12
%Y A223478 Cf. A223480.
%K A223478 nonn
%O A223478 1,1
%A A223478 _R. H. Hardin_, Mar 20 2013