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

1,2

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..160

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) +29600000*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

Example

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

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

Sequence in context: A067607 A013332 A223282 * A063871 A084316 A126810

Adjacent sequences: A223477 A223478 A223479 * A223481 A223482 A223483

Keyword

nonn,tabl

Author

R. H. Hardin Mar 20 2013

Status

approved