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A223284 Rolling icosahedron face footprints: number of 3 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

%I A223284 #9 Aug 18 2018 16:03:31
%S A223284 400,75,849,4995,38457,261819,1881441,13196979,93567177,660226923,
%T A223284 4668616305,32981553891,233097416793,1647108262683,11639737522305,
%U A223284 82252298336787,581246168781033,4107418513432011,29025468445135761
%N A223284 Rolling icosahedron face footprints: number of 3 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
%C A223284 Row 3 of A223282.
%H A223284 R. H. Hardin, <a href="/A223284/b223284.txt">Table of n, a(n) for n = 1..210</a>
%F A223284 Empirical: a(n) = 5*a(n-1) + 18*a(n-2) - 24*a(n-3) for n>4.
%F A223284 Empirical g.f.: x*(400 - 1925*x - 6726*x^2 + 9000*x^3) / (1 - 5*x - 18*x^2 + 24*x^3). - _Colin Barker_, Aug 18 2018
%e A223284 Some solutions for n=3:
%e A223284   0 2 3   0 1 0   0 5 7   0 5 9   0 1 0   0 1 6   0 5 9
%e A223284   8 2 3   6 1 4   9 5 9   0 5 9   4 1 6   0 1 4   9 5 9
%e A223284   8 2 3   6 1 0   7 5 9   0 5 9   6 1 4   4 1 0   7 5 9
%e A223284 Face neighbors:
%e A223284    0 ->  1  2  5
%e A223284    1 ->  0  4  6
%e A223284    2 ->  0  3  8
%e A223284    3 ->  2  4 16
%e A223284    4 ->  3  1 17
%e A223284    5 ->  0  7  9
%e A223284    6 ->  1  7 10
%e A223284    7 ->  6  5 11
%e A223284    8 ->  2  9 13
%e A223284    9 ->  8  5 14
%e A223284   10 ->  6 12 17
%e A223284   11 ->  7 12 14
%e A223284   12 -> 11 10 19
%e A223284   13 ->  8 15 16
%e A223284   14 ->  9 11 15
%e A223284   15 -> 14 13 19
%e A223284   16 ->  3 13 18
%e A223284   17 ->  4 10 18
%e A223284   18 -> 16 17 19
%e A223284   19 -> 15 18 12
%Y A223284 Cf. A223282.
%K A223284 nonn
%O A223284 1,1
%A A223284 _R. H. Hardin_, Mar 19 2013