A223186 T(n,k) = Rolling icosahedron footprints: number of n X k 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.

1, 5, 5, 25, 20, 25, 125, 80, 80, 125, 625, 320, 400, 320, 625, 3125, 1280, 2080, 2080, 1280, 3125, 15625, 5120, 10880, 14560, 10880, 5120, 15625, 78125, 20480, 56960, 103520, 103520, 56960, 20480, 78125, 390625, 81920, 298240, 738720, 1018720

Offset

1,2

Comments

Table starts

........1........5.........25.........125...........625.............3125

........5.......20.........80.........320..........1280.............5120

.......25.......80........400........2080.........10880............56960

......125......320.......2080.......14560........103520...........738720

......625.....1280......10880......103520.......1018720.........10117600

.....3125.....5120......56960......738720......10117600........141047120

....15625....20480.....298240.....5274720.....100734400.......1978496760

....78125....81920....1561600....37664800....1003652480......27809548920

...390625...327680....8176640...268947680...10001217120.....391129835720

..1953125..1310720...42813440..1920431520...99661921440....5502120113200

..9765625..5242880..224174080.13712917600..993129226400...77403634963000

.48828125.20971520.1173790720.97917648160.9896517562400.1088923059178480

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: a(n) = 6*a(n-1) -4*a(n-2) for n>3

k=4: a(n) = 10*a(n-1) -25*a(n-2) +36*a(n-3) -24*a(n-4) +4*a(n-5) for n>6

k=5: [order 12] for n>14

k=6: [order 34] for n>37

k=7: [order 88] for n>93

Example

Some solutions for n=3, k=4
..0..7..5.10....0..6..2..0....0..7..3.11....0..6..2..8....0..7..1..3
..5..0..6..5....2..4..6..2....5.11..7..5....5..0..1..2....1..0..7..1
..6..5..0..7....6..2..0..1...10..5.11.10....6..2..0..1....7..1..3..8
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

Crossrefs

Column 1 is A000351(n-1).

Column 2 is A003947.

Sequence in context: A255458 A256135 A227076 * A071340 A162962 A074872

Adjacent sequences: A223183 A223184 A223185 * A223187 A223188 A223189

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved