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A223481 Rolling icosahedron face footprints: number of 3 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. 1
400, 243, 2025, 16875, 147825, 1296675, 11374425, 99776475, 875239425, 7677601875, 67347938025, 590776238475, 5182290270225, 45459059955075, 398766959055225, 3497984511586875, 30684326686171425, 269162971152369075 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A223480.

LINKS

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

FORMULA

Empirical: a(n) = 9*a(n-1) - 2*a(n-2) for n>4.

Empirical g.f.: x*(400 - 3357*x + 638*x^2 - 864*x^3) / (1 - 9*x + 2*x^2). - Colin Barker, Aug 20 2018

EXAMPLE

Some solutions for n=3:

..0..2..3....0..1..0....0..2..8....0..5..0....0..1..0....0..2..0....0..1..6

..3..4..1....0..2..8....3..2..8....0..5..9....0..2..0....3..2..3....6..1..6

..1..4..1....8..2..8....8..9..5....9..8..2....3..2..8....3..4..1....6.10.12

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. A223480.

Sequence in context: A115470 A223284 A061042 * A037991 A200837 A250847

Adjacent sequences:  A223478 A223479 A223480 * A223482 A223483 A223484

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 20 2013

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)