A223208 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 or vertical neighbor moves across an icosahedral edge.

729, 46875, 3889953, 347696019, 31921015497, 2960941376139, 275769851453745, 25725360515161923, 2401334251012194777, 224209069529029889211, 20936162679299127225537, 1955051227721359130017011

Offset: 1

Author

R. H. Hardin Mar 18 2013

Keywords

• nonn

Comments

Column 7 of A223209

Examples

			Some solutions for n=3
..0..5..9..5..9..5..7....0..5..0..2..0..1..4....0..5..0..1..6..1..4
..5..0..5..0..5..9..5....5..0..2..0..5..0..1....5..0..1..0..1..4.17
..0..5..0..1..0..5..7....0..5..0..5..0..2..0....0..5..0..1..4.17..4
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
		

Links

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

Formula

Empirical: a(n) = 117*a(n-1) -614*a(n-2) -193608*a(n-3) +4171896*a(n-4) [phone]*a(n-5) -842180224*a(n-6) [phone]*a(n-7) [phone]*a(n-8) -356768428544*a(n-9) -786566761984*a(n-10) [phone]*a(n-11) -6785526038528*a(n-12) -118510105321472*a(n-13) [phone]*a(n-14) [phone]*a(n-15) -1309510355714048*a(n-16) -1087672042455040*a(n-17) +3564507406925824*a(n-18) [phone]*a(n-19) -4461650060509184*a(n-20) [phone]*a(n-21) +2549613680656384*a(n-22) -206006306996224*a(n-23) -619282299879424*a(n-24) [phone]*a(n-25) [phone]*a(n-26) -8245531901952*a(n-27) [phone]*a(n-28)