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 A223478 Rolling icosahedron face footprints: number of n X 6 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. 1

%I #8 Aug 20 2018 14:37:05

%S 243,16875,1296675,101331675,7939566675,622332801675,48783753036675,

%T 3824122400271675,299770559674506675,23498831496975741675,

%U 1842059141815703976675,144397899075877259211675

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

%H R. H. Hardin, <a href="/A223478/b223478.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 101*a(n-1) -1900*a(n-2) +10000*a(n-3).

%F Empirical g.f.: 27*x*(9 - 284*x + 2000*x^2) / (1 - 101*x + 1900*x^2 - 10000*x^3). - _Colin Barker_, Aug 20 2018

%e Some solutions for n=3:

%e ..0..1..6..1..4..3....0..1..4..1..4..1....0..1..0..5..9..8....0..1..0..2..3.16

%e ..0..1..0..1..4..1....0..1..4..1..4..3....0..5..9..5..9..5....0..2..0..2..3.16

%e ..0..1..4..1..6..1....6..1..4..3..2..0....0..5..9.14..9.14....0..2..3..4..3..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

%Y Cf. A223480.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 20 2013

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Last modified December 5 23:11 EST 2023. Contains 367594 sequences. (Running on oeis4.)