A223263 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 vertical neighbor moves along an icosahedral edge

1, 5, 5, 25, 65, 25, 125, 845, 845, 125, 625, 10985, 28885, 10985, 625, 3125, 142805, 988625, 988625, 142805, 3125, 15625, 1856465, 33841585, 89405945, 33841585, 1856465, 15625, 78125, 24134045, 1158447605, 8093320565, 8093320565

Offset

1,2

Comments

Table starts

.....1.........5............25..............125..................625

.....5........65...........845............10985...............142805

....25.......845.........28885...........988625.............33841585

...125.....10985........988625.........89405945...........8093320565

...625....142805......33841585.......8093320565........1940359745365

..3125...1856465....1158447605.....732779276465......465517850602985

.15625..24134045...39655444525...66349405785905...111705181963446505

.78125.313742585.1357467150905.6007647236699705.26806081975380034085

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1)

k=2: a(n) = 13*a(n-1)

k=3: a(n) = 38*a(n-1) -129*a(n-2)

k=4: a(n) = 118*a(n-1) -2675*a(n-2) +17534*a(n-3) -37105*a(n-4) +10948*a(n-5) +20013*a(n-6)

k=5: [order 20]

Example

Some solutions for n=3 k=4
..0..5..6..2....0..6..5..7....0..7..5..0....0..6..0..7....0..2..1..0
..6..0..2..0....6..4..6..5....6..5.10..5....6.10..5..0....6..0..7..1
..0..7..0..1....0..6..5..0....0..7..5..0...10..6.10..5....4..6..0..2
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 A000351(n-1)

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

Sequence in context: A263798 A257607 A093643 * A189318 A257615 A257624

Adjacent sequences: A223260 A223261 A223262 * A223264 A223265 A223266

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved