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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
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 1 is A001021(n-1)
Column 2 is 5*13^(n-1)
Row 1 is A000351(n-1)
Sequence in context: A301748 A108201 A289586 * A038254 A223321 A073095
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 18 2013
STATUS
approved