A223209 T(n,k)=Rolling icosahedron face footprints: number of nXk 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

1, 3, 3, 9, 15, 9, 27, 75, 75, 27, 81, 375, 657, 375, 81, 243, 1875, 5763, 5763, 1875, 243, 729, 9375, 50553, 90111, 50553, 9375, 729, 2187, 46875, 443451, 1412907, 1412907, 443451, 46875, 2187, 6561, 234375, 3889953, 22163655, 39868737, 22163655

Offset

1,2

Comments

Table starts

......1.........3............9..............27.................81

......3........15...........75.............375...............1875

......9........75..........657............5763..............50553

.....27.......375.........5763...........90111............1412907

.....81......1875........50553.........1412907...........39868737

....243......9375.......443451........22163655.........1127761923

....729.....46875......3889953.......347696019........31921015497

...2187....234375.....34122675......5454600015.......903661481115

...6561...1171875....299324169.....85571052219.....25583075832465

..19683...5859375...2625672171...1342427863959....724276345970163

..59049..29296875..23032401201..21059839795875..20504869741550745

.177147.146484375.202040266467.330384125138847.580510427181846027

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 5*a(n-1)

k=3: a(n) = 9*a(n-1) -2*a(n-2)

k=4: a(n) = 19*a(n-1) -54*a(n-2) +32*a(n-3)

k=5: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7)

k=6: [order 12]

k=7: [order 28]

Example

Some solutions for n=3 k=4
..0..2..0..1....0..2..0..2....0..5..0..2....0..2..3..4....0..1..6.10
..2..8..2..0....2..8..2..8....5..9..5..0....2..0..2..3....1..6..1..6
..3..2..3..2....3..2..8.13....0..5..0..5....0..2..8..2....4..1..4..1
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

Column 1 is A000244(n-1)

Column 2 is A005053

Sequence in context: A122847 A197462 A264098 * A233026 A105423 A147471

Adjacent sequences: A223206 A223207 A223208 * A223210 A223211 A223212

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved