login
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.
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 18 2013
STATUS
approved