A223285 Rolling icosahedron face footprints: number of 4 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.

8000, 375, 8295, 72279, 1024071, 10979127, 137621799, 1576368663, 19009505799, 222545715447, 2650002132711, 31248496329687, 370552575553479, 4379948164268727, 51867287743753383, 613557282050858391

Offset

1,1

Comments

Row 4 of A223282.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 92*a(n-2) - 56*a(n-3) - 920*a(n-4) + 192*a(n-5) + 1152*a(n-6) for n>7.

Empirical g.f.: x*(8000 - 39625*x - 729580*x^2 + 444304*x^3 + 7280536*x^4 - 1517376*x^5 - 9097344*x^6) / (1 - 5*x - 92*x^2 + 56*x^3 + 920*x^4 - 192*x^5 - 1152*x^6). - Colin Barker, Aug 18 2018

Example

Some solutions for n=3:
  0 1 0   0 2 0   0 2 8   0 5 7   0 1 4   0 2 3   0 1 4
  4 1 4   0 2 8   8 2 3   9 5 9   4 1 0   8 2 0   6 1 6
  6 1 4   0 2 3   0 2 8   9 5 0   0 1 6   0 2 8   6 1 6
  6 1 0   8 2 8   3 2 0   9 5 0   6 1 6   0 2 8   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: A126893 A217068 A043614 * A223482 A224647 A013813

Adjacent sequences: A223282 A223283 A223284 * A223286 A223287 A223288

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved