A223287 Rolling icosahedron face footprints: number of 6 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.

3200000, 9375, 792087, 15229647, 792881031, 20570223999, 879050854455, 26073158735535, 1008694505830119, 32094483162308319, 1178050642133703831, 38926413103761206799, 1389205962179205980487, 46849778740107421135935

Offset

1,1

Comments

Row 6 of A223282.

Links

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

Formula

Empirical: a(n) = 13*a(n-1) +1244*a(n-2) -8256*a(n-3) -402464*a(n-4) +1780288*a(n-5) +55907168*a(n-6) -197740288*a(n-7) -4040907520*a(n-8) +12437493760*a(n-9) +166070886400*a(n-10) -452922138624*a(n-11) -4093663121408*a(n-12) +9761715879936*a(n-13) +62363887337472*a(n-14) -126220206735360*a(n-15) -595038449696768*a(n-16) +978337484767232*a(n-17) +3542610027216896*a(n-18) -4455273209004032*a(n-19) -12803732509032448*a(n-20) +11344509988241408*a(n-21) +26381276122447872*a(n-22) -14571020149063680*a(n-23) -27374953313599488*a(n-24) +7085252929388544*a(n-25) +10449758510383104*a(n-26) for n>27.

Example

Some solutions for n=3
..0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0
..0..5..9....7..5..9....0..5..0....7..5..9....9..5..9....0..5..9....9..5..7
..7..5..0....7..5..7....9..5..9....0..5..7....7..5..0....7..5..0....9..5..7
..0..5..9....0..5..9....9..5..9....9..5..9....9..5..0....9..5..9....7..5..0
..9..5..0....7..5..0....9..8..9....9..5..0....7..5..0....9.14..9....7..5..7
..9..5..9....0..5..9...13..8..2....7..5..9....7..5..7...11.14..9....7..5..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: A153750 A234689 A232619 * A223484 A029820 A146976

Adjacent sequences: A223284 A223285 A223286 * A223288 A223289 A223290

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved