A223206 - OEIS

%I #4 Mar 18 2013 07:46:32

%S 81,1875,50553,1412907,39868737,1127761923,31921015497,903661481115,

%T 25583075832465,724276345970163,20504869741550745,580510427181846027,

%U 16434750355138945761,465281963351360897763,13172534004090254190441

%N Rolling icosahedron face footprints: number of nX5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge

%C Column 5 of A223209

%H R. H. Hardin, <a href="/A223206/b223206.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7)

%e Some solutions for n=3

%e ..0..1..4..3..4....0..2..0..2..0....0..1..0..2..3....0..2..0..1..6

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

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

%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

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 18 2013