A223279 - OEIS

A223279

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, diagonal or antidiagonal neighbor moves across an icosahedral edge.

%I #10 Aug 18 2018 17:34:04

%S 81,1575,38457,1024071,28271577,792881031,22392745881,634400697159,

%T 17998034165721,510923724667143,14507984391789081,412013548109024967,

%U 11701449873880124505,332336795068373382279,9438910778776181239449

%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, diagonal or antidiagonal neighbor moves across an icosahedral edge.

%C Column 5 of A223282.

%H R. H. Hardin, <a href="/A223279/b223279.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 45*a(n-1) - 518*a(n-2) + 1268*a(n-3) + 1704*a(n-4) - 4064*a(n-5) + 1536*a(n-6).

%F Empirical g.f.: 3*x*(9 - 68*x + 64*x^2)*(3 - 54*x - 76*x^2 + 56*x^3) / (1 - 45*x + 518*x^2 - 1268*x^3 - 1704*x^4 + 4064*x^5 - 1536*x^6). - _Colin Barker_, Aug 18 2018

%e Some solutions for n=3:

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

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

%e 0 1 0 1 6 9 5 0 5 9 9 5 0 2 3 6 1 6 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. A223282.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013