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A223321 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 antidiagonal neighbor moves along an icosahedral edge 9
1, 5, 12, 25, 125, 144, 125, 1625, 3125, 1728, 625, 21125, 105625, 78125, 20736, 3125, 274625, 3570125, 6865625, 1953125, 248832, 15625, 3570125, 122039125, 603351125, 446265625, 48828125, 2985984, 78125, 46411625, 4176940625, 54279694625 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

.......12.........125............1625..............21125.................274625

......144........3125..........105625............3570125..............122039125

.....1728.......78125.........6865625..........603351125............54279694625

....20736.....1953125.......446265625.......101966340125.........24143758634125

...248832....48828125.....29007265625.....17232311481125......10739266230499625

..2985984..1220703125...1885472265625...2912260640310125....4776881955584279125

.35831808.30517578125.122555697265625.492172048212411125.2124782217358970404625

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) = 25*a(n-1)

k=3: a(n) = 65*a(n-1)

k=4: a(n) = 169*a(n-1)

k=5: a(n) = 479*a(n-1) -15210*a(n-2)

k=6: a(n) = 1366*a(n-1) -232713*a(n-2) +9253764*a(n-3)

k=7: [order 8]

Empirical for row n:

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

n=2: a(n) = 13*a(n-1) for n>2

n=3: a(n) = 38*a(n-1) -129*a(n-2) for n>4

n=4: [order 7] for n>10

n=5: [order 32] for n>36

EXAMPLE

Some solutions for n=3 k=4

..0..1..8..9....0..1..0..7....0..1..0..2....0..1..0..6....0..6..2..4

..0..2..8..2....0..5..0..5....0..6..0..2....0..6.10..5....0..1..2..4

..6..2..4..2....0..1..0..7....0..7..0..7....0..6.10..5....0..6.10..4

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 A013710(n-1)

Column 3 is 25*65^(n-1)

Column 4 is 125*169^(n-1)

Row 1 is A000351(n-1)

Sequence in context: A289586 A223233 A038254 * A073095 A309323 A294017

Adjacent sequences:  A223318 A223319 A223320 * A223322 A223323 A223324

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 19 2013

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)