A223477 - OEIS

%I #8 Aug 20 2018 13:30:45

%S 81,3375,147825,6526575,288507825,12755926575,563999907825,

%T 24937217326575,1102598111307825,48751338478726575,

%U 2155538829022707825,95307078736540126575,4213999366856734107825,186321844088731401526575

%N Rolling icosahedron face footprints: number of n X 5 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 Column 5 of A223480.

%H R. H. Hardin, <a href="/A223477/b223477.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 51*a(n-1) - 300*a(n-2).

%F Empirical g.f.: 27*x*(3 - 28*x) / (1 - 51*x + 300*x^2). - _Colin Barker_, Aug 20 2018

%e Some solutions for n=3:

%e ..0..1..6.10.17....0..1..6..7..5....0..2..0..2..0....0..2..0..1..6

%e ..6.10.17.10.12....6..7.11..7..6....8..2..0..5..7....0..1..0..1..4

%e .17.10.12.11.12....6..7..5..7..5....0..5..7.11.14....0..5..0..1..6

%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