A223481 - OEIS

%I #8 Aug 20 2018 14:38:27

%S 400,243,2025,16875,147825,1296675,11374425,99776475,875239425,

%T 7677601875,67347938025,590776238475,5182290270225,45459059955075,

%U 398766959055225,3497984511586875,30684326686171425,269162971152369075

%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 or antidiagonal neighbor moves across an icosahedral edge.

%C Row 3 of A223480.

%H R. H. Hardin, <a href="/A223481/b223481.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 2*a(n-2) for n>4.

%F Empirical g.f.: x*(400 - 3357*x + 638*x^2 - 864*x^3) / (1 - 9*x + 2*x^2). - _Colin Barker_, Aug 20 2018

%e Some solutions for n=3:

%e ..0..2..3....0..1..0....0..2..8....0..5..0....0..1..0....0..2..0....0..1..6

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

%e ..1..4..1....8..2..8....8..9..5....9..8..2....3..2..8....3..4..1....6.10.12

%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. A223480.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 20 2013