cp's OEIS Frontend

A223283 Rolling icosahedron face footprints: number of 2 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 A223283 #10 Aug 18 2018 17:33:51
%S A223283 20,15,87,351,1575,6831,29943,130815,572103,2501199,10936215,47815839,
%T A223283 209064807,914089455,3996657207,17474508351,76403468295,334057454991,
%U A223283 1460593174743,6386124254175,27921931810983,122082540957999
%N A223283 Rolling icosahedron face footprints: number of 2 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 A223283 Row 2 of A223282.
%H A223283 R. H. Hardin, <a href="/A223283/b223283.txt">Table of n, a(n) for n = 1..210</a>
%F A223283 Empirical: a(n) = 3*a(n-1) + 6*a(n-2) for n>3.
%F A223283 Empirical g.f.: x*(20 - 45*x - 78*x^2) / (1 - 3*x - 6*x^2). - _Colin Barker_, Aug 18 2018
%e A223283 Some solutions for n=3:
%e A223283   0 1 4   0 1 4   0 5 0   0 1 6   0 1 0   0 5 7   0 1 6
%e A223283   4 1 0   4 1 4   7 5 7   0 1 4   0 5 0   9 5 0   4 1 0
%e A223283 Face neighbors:
%e A223283    0 ->  1  2  5
%e A223283    1 ->  0  4  6
%e A223283    2 ->  0  3  8
%e A223283    3 ->  2  4 16
%e A223283    4 ->  3  1 17
%e A223283    5 ->  0  7  9
%e A223283    6 ->  1  7 10
%e A223283    7 ->  6  5 11
%e A223283    8 ->  2  9 13
%e A223283    9 ->  8  5 14
%e A223283   10 ->  6 12 17
%e A223283   11 ->  7 12 14
%e A223283   12 -> 11 10 19
%e A223283   13 ->  8 15 16
%e A223283   14 ->  9 11 15
%e A223283   15 -> 14 13 19
%e A223283   16 ->  3 13 18
%e A223283   17 ->  4 10 18
%e A223283   18 -> 16 17 19
%e A223283   19 -> 15 18 12
%Y A223283 Cf. A223282.
%K A223283 nonn
%O A223283 1,1
%A A223283 _R. H. Hardin_, Mar 19 2013