A223281 Rolling icosahedron face footprints: number of nX7 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

729, 29943, 1881441, 137621799, 10801441521, 879050854455, 72981761306721, 6127190749734087, 517631500569076305, 43882777288012073559, 3727442176083442555713, 316954431035692378210023

Offset

1,1

Comments

Column 7 of A223282

Links

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

Formula

Empirical: a(n) = 193*a(n-1) -13138*a(n-2) +389164*a(n-3) -4361048*a(n-4) -16478976*a(n-5) +680367552*a(n-6) -2205737728*a(n-7) -32395676672*a(n-8) +159364997888*a(n-9) +669407522304*a(n-10) -3582601411584*a(n-11) -5951537518592*a(n-12) +34040410587136*a(n-13) +16838602686464*a(n-14) -137580342149120*a(n-15) +18193951227904*a(n-16) +210744868077568*a(n-17) -92999396622336*a(n-18) -80015240724480*a(n-19) +37572373905408*a(n-20)

Example

Some solutions for n=3
..0..1..0..2..3..4..3....0..1..0..2..8..2..0....0..1..4..3.16..3.16
..0..1..0..2..3..4.17....0..5..0..2..0..2..3....0..1..4..3..2..3..2
..0..1..0..2..3..4..1....0..5..0..2..8..2..8....0..1..4..3..2..8..2
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

Sequence in context: A232028 A203651 A036536 * A268976 A224357 A016770

Adjacent sequences: A223278 A223279 A223280 * A223282 A223283 A223284

Keyword

nonn

Author

R. H. Hardin Mar 19 2013

Status

approved