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.

400, 75, 849, 4995, 38457, 261819, 1881441, 13196979, 93567177, 660226923, 4668616305, 32981553891, 233097416793, 1647108262683, 11639737522305, 82252298336787, 581246168781033, 4107418513432011, 29025468445135761

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: A140892 A115470 A356821 * A061042 A223481 A037991

Adjacent sequences: A223281 A223282 A223283 * A223285 A223286 A223287

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved