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

Author

R. H. Hardin Mar 18 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000351(n-1).

Column 2 is A003947.

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