|
|
A223233
|
|
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, diagonal or antidiagonal neighbor moves along an icosahedral edge
|
|
11
|
|
|
1, 5, 12, 25, 65, 144, 125, 785, 845, 1728, 625, 7445, 25225, 10985, 20736, 3125, 75665, 492365, 812225, 142805, 248832, 15625, 753005, 11043445, 32837285, 26157625, 1856465, 2985984, 78125, 7540985, 236027705, 1697263985, 2191464605, 842416625
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Table starts
............1.............5................25.................125
...........12............65...............785................7445
..........144...........845.............25225..............492365
.........1728.........10985............812225............32837285
........20736........142805..........26157625..........2191464605
.......248832.......1856465.........842416625........146259564725
......2985984......24134045.......27130395625.......9761484584045
.....35831808.....313742585......873746350625.....651489782832965
....429981696....4078653605....28139386665625...43480983274973885
...5159780352...53022496865...906241361740625.2901957882023749205
..61917364224..689292459245.29185902861015625
.743008370688.8960801970185
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 12*a(n-1)
k=2: a(n) = 13*a(n-1)
k=3: a(n) = 35*a(n-1) -90*a(n-2)
k=4: a(n) = 73*a(n-1) -423*a(n-2) +351*a(n-3)
k=5: [order 11]
k=6: [order 26]
Empirical for row n:
n=1: a(n) = 5*a(n-1)
n=2: a(n) = 7*a(n-1) +30*a(n-2) for n>3
n=3: a(n) = 18*a(n-1) +103*a(n-2) -552*a(n-3) +540*a(n-4) for n>5
n=4: a(n) = [order 12] for n>13
|
|
EXAMPLE
|
Some solutions for n=3 k=4
..0..6..0..5....0..5..6..5....0..7..0..1....0..1..3..1....0..1..0..7
..0..6.10..5....0..5..6..5....3..7..0..7....3..7..3..9....0..7..0..7
..0..5.10..4....6..2..6..5....3..7..5..7....3..9.11..7....3..1..3..7
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 2 is 5*13^(n-1)
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|