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

Author

R. H. Hardin Mar 18 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A001021(n-1)

Column 2 is 5*13^(n-1)

Row 1 is A000351(n-1)

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