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

Author

R. H. Hardin Mar 19 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A009964(n-1)

Column 2 is A005053

Row 1 is A000244(n-1)

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