A223284 - OEIS

%I #9 Aug 18 2018 16:03:31

%S 400,75,849,4995,38457,261819,1881441,13196979,93567177,660226923,

%T 4668616305,32981553891,233097416793,1647108262683,11639737522305,

%U 82252298336787,581246168781033,4107418513432011,29025468445135761

%N 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 Row 3 of A223282.

%H R. H. Hardin, <a href="/A223284/b223284.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 18*a(n-2) - 24*a(n-3) for n>4.

%F 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 Some solutions for n=3:

%e   0 2 3   0 1 0   0 5 7   0 5 9   0 1 0   0 1 6   0 5 9

%e   8 2 3   6 1 4   9 5 9   0 5 9   4 1 6   0 1 4   9 5 9

%e   8 2 3   6 1 0   7 5 9   0 5 9   6 1 4   4 1 0   7 5 9

%e Face neighbors:

%e    0 ->  1  2  5

%e    1 ->  0  4  6

%e    2 ->  0  3  8

%e    3 ->  2  4 16

%e    4 ->  3  1 17

%e    5 ->  0  7  9

%e    6 ->  1  7 10

%e    7 ->  6  5 11

%e    8 ->  2  9 13

%e    9 ->  8  5 14

%e   10 ->  6 12 17

%e   11 ->  7 12 14

%e   12 -> 11 10 19

%e   13 ->  8 15 16

%e   14 ->  9 11 15

%e   15 -> 14 13 19

%e   16 ->  3 13 18

%e   17 ->  4 10 18

%e   18 -> 16 17 19

%e   19 -> 15 18 12

%Y Cf. A223282.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013