A223484 - OEIS

%I #6 Oct 02 2021 10:28:49

%S 3200000,177147,6834375,263671875,12755926575,622332801675,

%T 31621425535575,1608341612382675,82456836767805375,

%U 4227484231555443675,217015136003889260775,11140133589863412595875,571949483621302897613775

%N Rolling icosahedron face footprints: number of 6 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 6 of A223480.

%H R. H. Hardin, <a href="/A223484/b223484.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 65*a(n-1) -392*a(n-2) -21060*a(n-3) +271696*a(n-4) -61920*a(n-5) -12301824*a(n-6) +41001664*a(n-7) +141738752*a(n-8) -796132352*a(n-9) -244873216*a(n-10) +5515101184*a(n-11) -3510669312*a(n-12) -15177555968*a(n-13) +15458697216*a(n-14) +13446168576*a(n-15) -14442954752*a(n-16) -4507631616*a(n-17) +3989831680*a(n-18) +252706816*a(n-19) -251658240*a(n-20) for n>25.

%e Some solutions for n=3

%e ..0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0

%e ..0..1..0....0..1..0....0..1..0....0..1..4....0..1..4....0..1..0....0..1..4

%e ..0..1..4....6..1..0....6..1..4....4.17..4....4..1..4....4..1..6....0..1..4

%e ..4..1..0....0..5..9....4..1..0...10.17.10....4.17.18....0..1..4....0..1..0

%e ..0..1..4....9..5..0....4..1..6....4.17.10...18.16.18....4.17.10....0..1..4

%e ..0..1..4....0..2..3....6..7..5....4.17.10...18.17..4...10.12.10....4..3.16

%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