A223282 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, diagonal or antidiagonal neighbor moves across an icosahedral edge

1, 3, 20, 9, 15, 400, 27, 87, 75, 8000, 81, 351, 849, 375, 160000, 243, 1575, 4995, 8295, 1875, 3200000, 729, 6831, 38457, 72279, 81057, 9375, 64000000, 2187, 29943, 261819, 1024071, 1048923, 792087, 46875, 1280000000, 6561, 130815, 1881441, 10979127

Offset

1,2

Comments

Table starts

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

...........20......15.........87..........351............1575..............6831

..........400......75........849.........4995...........38457............261819

.........8000.....375.......8295........72279.........1024071..........10979127

.......160000....1875......81057......1048923........28271577.........473368227

......3200000....9375.....792087.....15229647.......792881031.......20570223999

.....64000000...46875....7740273....221142771.....22392745881......895927195659

...1280000000..234375...75637959...3211159815....634400697159....39047604482055

..25600000000.1171875..739134273..46628577099..17998034165721..1702160040384051

.512000000000.5859375.7222821495.677084057343.510923724667143.74204651599582287

Links

R. H. Hardin, Table of n, a(n) for n = 1..161

Formula

Empirical for column k:

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

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

k=3: a(n) = 11*a(n-1) -12*a(n-2)

k=4: a(n) = 17*a(n-1) -36*a(n-2)

k=5: a(n) = 45*a(n-1) -518*a(n-2) +1268*a(n-3) +1704*a(n-4) -4064*a(n-5) +1536*a(n-6)

k=6: [order 9]

k=7: [order 20]

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) +6*a(n-2) for n>3

n=3: a(n) = 5*a(n-1) +18*a(n-2) -24*a(n-3) for n>4

n=4: a(n) = 5*a(n-1) +92*a(n-2) -56*a(n-3) -920*a(n-4) +192*a(n-5) +1152*a(n-6) for n>7

n=5: [order 12] for n>13

n=6: [order 26] for n>27

Example

Some solutions for n=3 k=4
..0..5..0..5....0..5..0..5....0..5..0..5....0..2..0..2....0..5..7..5
..0..2..0..5....0..2..0..5....0..5..0..1....0..2..0..2....7..5..0..5
..8..2..0..2....3..2..0..1....0..2..0..2....0..5..0..2....9..5..0..2
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 A005053

Row 1 is A000244(n-1)

Sequence in context: A260371 A067607 A013332 * A223480 A063871 A084316

Adjacent sequences: A223279 A223280 A223281 * A223283 A223284 A223285

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved