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

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

R. H. Hardin, Table of n, a(n) for n = 1..97

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

Adjacent sequences: A223230 A223231 A223232 * A223234 A223235 A223236

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved