A223480 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 antidiagonal neighbor moves across an icosahedral edge.

1, 3, 20, 9, 27, 400, 27, 135, 243, 8000, 81, 675, 2025, 2187, 160000, 243, 3375, 16875, 30375, 19683, 3200000, 729, 16875, 147825, 421875, 455625, 177147, 64000000, 2187, 84375, 1296675, 6526575, 10546875, 6834375, 1594323, 1280000000, 6561, 421875

Offset: 1

Author

R. H. Hardin Mar 20 2013

Keywords

• nonn
• tabl

Comments

Table starts

..........1........3..........9...........27.............81..............243

.........20.......27........135..........675...........3375............16875

........400......243.......2025........16875.........147825..........1296675

.......8000.....2187......30375.......421875........6526575........101331675

.....160000....19683.....455625.....10546875......288507825.......7939566675

....3200000...177147....6834375....263671875....12755926575.....622332801675

...64000000..1594323..102515625...6591796875...563999907825...48783753036675

.1280000000.14348907.1537734375.164794921875.24937217326575.3824122400271675

Examples

			Some solutions for n=3 k=4
..0..1..6.10....0..1..4..1....0..1..0..1....0..2..8.13....0..2..8..9
..6..1..6..1....6..1..4..3....4..1..0..5....0..2..8..2....8..9..8..9
..4..1..4..3....4.17..4.17....0..5..9..5....8..2..3..4....8..2..8..9
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..160

Crossrefs

Column 1 is A009964(n-1)

Column 2 is A013708(n-1)

Column 3 is 9*15^(n-1)

Column 4 is 27*25^(n-1)

Row 1 is A000244(n-1)

Row 2 is 27*5^(n-2) for n>1

Formula

Empirical for column k:

k=1: a(n) = 20*a(n-1)

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

k=3: a(n) = 15*a(n-1)

k=4: a(n) = 25*a(n-1)

k=5: a(n) = 51*a(n-1) -300*a(n-2)

k=6: a(n) = 101*a(n-1) -1900*a(n-2) +10000*a(n-3)

k=7: a(n) = 227*a(n-1) -14764*a(n-2) +411840*a(n-3) -5347200*a(n-4) [phone]*a(n-5) -48000000*a(n-6)

Empirical for row n:

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

n=2: a(n) = 5*a(n-1) for n>2

n=3: a(n) = 9*a(n-1) -2*a(n-2) for n>4

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

n=5: a(n) = 33*a(n-1) -86*a(n-2) -1564*a(n-3) +7040*a(n-4) -6480*a(n-5) -5088*a(n-6) +5824*a(n-7) -512*a(n-8) for n>13

n=6: [order 20] for n>25