A223283 Rolling icosahedron face footprints: number of 2 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.

20, 15, 87, 351, 1575, 6831, 29943, 130815, 572103, 2501199, 10936215, 47815839, 209064807, 914089455, 3996657207, 17474508351, 76403468295, 334057454991, 1460593174743, 6386124254175, 27921931810983, 122082540957999

Offset

1,1

Comments

Row 2 of A223282.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 6*a(n-2) for n>3.

Empirical g.f.: x*(20 - 45*x - 78*x^2) / (1 - 3*x - 6*x^2). - Colin Barker, Aug 18 2018

Example

Some solutions for n=3:
  0 1 4   0 1 4   0 5 0   0 1 6   0 1 0   0 5 7   0 1 6
  4 1 0   4 1 4   7 5 7   0 1 4   0 5 0   9 5 0   4 1 0
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: A215028 A292558 A040382 * A327788 A365065 A076119

Adjacent sequences: A223280 A223281 A223282 * A223284 A223285 A223286

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved