|
| |
|
|
A223321
|
|
T(n,k)=Rolling icosahedron footprints: number of nXk 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge
|
|
9
|
|
|
|
1, 5, 12, 25, 125, 144, 125, 1625, 3125, 1728, 625, 21125, 105625, 78125, 20736, 3125, 274625, 3570125, 6865625, 1953125, 248832, 15625, 3570125, 122039125, 603351125, 446265625, 48828125, 2985984, 78125, 46411625, 4176940625, 54279694625
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Table starts
........1...........5..............25................125....................625
.......12.........125............1625..............21125.................274625
......144........3125..........105625............3570125..............122039125
.....1728.......78125.........6865625..........603351125............54279694625
....20736.....1953125.......446265625.......101966340125.........24143758634125
...248832....48828125.....29007265625.....17232311481125......10739266230499625
..2985984..1220703125...1885472265625...2912260640310125....4776881955584279125
.35831808.30517578125.122555697265625.492172048212411125.2124782217358970404625
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 12*a(n-1)
k=2: a(n) = 25*a(n-1)
k=3: a(n) = 65*a(n-1)
k=4: a(n) = 169*a(n-1)
k=5: a(n) = 479*a(n-1) -15210*a(n-2)
k=6: a(n) = 1366*a(n-1) -232713*a(n-2) +9253764*a(n-3)
k=7: [order 8]
Empirical for row n:
n=1: a(n) = 5*a(n-1)
n=2: a(n) = 13*a(n-1) for n>2
n=3: a(n) = 38*a(n-1) -129*a(n-2) for n>4
n=4: [order 7] for n>10
n=5: [order 32] for n>36
|
|
|
EXAMPLE
|
Some solutions for n=3 k=4
..0..1..8..9....0..1..0..7....0..1..0..2....0..1..0..6....0..6..2..4
..0..2..8..2....0..5..0..5....0..6..0..2....0..6.10..5....0..1..2..4
..6..2..4..2....0..1..0..7....0..7..0..7....0..6.10..5....0..6.10..4
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 3 is 25*65^(n-1)
Column 4 is 125*169^(n-1)
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
