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A223284 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, diagonal or antidiagonal neighbor moves across an icosahedral edge. 1
400, 75, 849, 4995, 38457, 261819, 1881441, 13196979, 93567177, 660226923, 4668616305, 32981553891, 233097416793, 1647108262683, 11639737522305, 82252298336787, 581246168781033, 4107418513432011, 29025468445135761 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A223282.

LINKS

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

FORMULA

Empirical: a(n) = 5*a(n-1) + 18*a(n-2) - 24*a(n-3) for n>4.

Empirical g.f.: x*(400 - 1925*x - 6726*x^2 + 9000*x^3) / (1 - 5*x - 18*x^2 + 24*x^3). - Colin Barker, Aug 18 2018

EXAMPLE

Some solutions for n=3:

  0 2 3   0 1 0   0 5 7   0 5 9   0 1 0   0 1 6   0 5 9

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

  8 2 3   6 1 0   7 5 9   0 5 9   6 1 4   4 1 0   7 5 9

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: A283384 A140892 A115470 * A061042 A223481 A037991

Adjacent sequences:  A223281 A223282 A223283 * A223285 A223286 A223287

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved

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Last modified September 19 16:34 EDT 2021. Contains 347564 sequences. (Running on oeis4.)