A223482 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 or antidiagonal neighbor moves across an icosahedral edge.

8000, 2187, 30375, 421875, 6526575, 101331675, 1588785975, 24919035075, 390919514175, 6132664672875, 96208422848775, 1509305488830675, 23677794878309775, 371454275512532475, 5827328087571285975

Offset: 1

Author

R. H. Hardin, Mar 20 2013

Keywords

• nonn

Comments

Row 4 of A223480.

Examples

			Some solutions for n=3:
..0..2..3....0..5..9....0..2..8....0..5..9....0..1..6....0..2..3....0..1..4
..0..2..8....7..5..7....3..2..8....9..5..7....6.10..6....8..2..0....0..1..6
..8..2..0....7..6..1....0..2..8....7..6..7....6..7..6....0..1..6....6..7.11
..8..2..8....7..6..7....8..2..8....7..5..9....6.10.12....6..1..0....6..7..6
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

Crossrefs

Cf. A223480.

Formula

Empirical: a(n) = 17*a(n-1) - 16*a(n-2) - 76*a(n-3) + 64*a(n-4) for n>7.

Empirical g.f.: x*(8000 - 133813*x + 121196*x^2 + 548492*x^3 - 505088*x^4 - 701568*x^5 + 691200*x^6) / ((1 + 2*x)*(1 - 19*x + 54*x^2 - 32*x^3)). - Colin Barker, Aug 20 2018