A223277 - OEIS

A223277

Rolling icosahedron face footprints: number of n X 3 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.

9, 87, 849, 8295, 81057, 792087, 7740273, 75637959, 739134273, 7222821495, 70581425169, 689721818919, 6739962906081, 65862930139863, 643612676665521, 6289384281642375, 61459874978079873, 600586013379170103

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OFFSET

1,1

COMMENTS

Column 3 of A223282.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 11*a(n-1) - 12*a(n-2).

Conjectures from Colin Barker, Aug 18 2018: (Start)

G.f.: 3*x*(3 - 4*x) / (1 - 11*x + 12*x^2).

a(n) = (2^(-1-n)*((11-sqrt(73))^n*(-7+sqrt(73)) + (7+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).

(End)

EXAMPLE

Some solutions for n=3:

..0..2..3....0..2..3....0..1..4....0..5..9....0..1..6....0..2..0....0..5..9

..0..2..3....8..2..3....0..1..4....0..5..0....0..1..0....3..2..8....9..5..9

..0..2..8....0..2..8....0..1..4....0..1..0....4..1..4....3..2..8....0..5..7

Face neighbors:

0 -> 1 2 5

1 -> 0 4 6

2 -> 0 3 8

3 -> 2 4 16

4 -> 3 1 17

5 -> 0 7 9

6 -> 1 7 10

7 -> 6 5 11

8 -> 2 9 13

9 -> 8 5 14

10 -> 6 12 17

11 -> 7 12 14

12 -> 11 10 19

13 -> 8 15 16

14 -> 9 11 15

15 -> 14 13 19

16 -> 3 13 18

17 -> 4 10 18

18 -> 16 17 19

19 -> 15 18 12

CROSSREFS

Cf. A223282.

Sequence in context: A219123 A144852 A153191 * A267265 A152264 A035101

Adjacent sequences: A223274 A223275 A223276 * A223278 A223279 A223280

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved