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A223209 T(n,k)=Rolling icosahedron face footprints: number of nXk 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge 7
1, 3, 3, 9, 15, 9, 27, 75, 75, 27, 81, 375, 657, 375, 81, 243, 1875, 5763, 5763, 1875, 243, 729, 9375, 50553, 90111, 50553, 9375, 729, 2187, 46875, 443451, 1412907, 1412907, 443451, 46875, 2187, 6561, 234375, 3889953, 22163655, 39868737, 22163655 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

......1.........3............9..............27.................81

......3........15...........75.............375...............1875

......9........75..........657............5763..............50553

.....27.......375.........5763...........90111............1412907

.....81......1875........50553.........1412907...........39868737

....243......9375.......443451........22163655.........1127761923

....729.....46875......3889953.......347696019........31921015497

...2187....234375.....34122675......5454600015.......903661481115

...6561...1171875....299324169.....85571052219.....25583075832465

..19683...5859375...2625672171...1342427863959....724276345970163

..59049..29296875..23032401201..21059839795875..20504869741550745

.177147.146484375.202040266467.330384125138847.580510427181846027

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 9*a(n-1) -2*a(n-2)

k=4: a(n) = 19*a(n-1) -54*a(n-2) +32*a(n-3)

k=5: a(n) = 31*a(n-1) -24*a(n-2) -1612*a(n-3) +3816*a(n-4) +1152*a(n-5) -2784*a(n-6) +256*a(n-7)

k=6: [order 12]

k=7: [order 28]

EXAMPLE

Some solutions for n=3 k=4

..0..2..0..1....0..2..0..2....0..5..0..2....0..2..3..4....0..1..6.10

..2..8..2..0....2..8..2..8....5..9..5..0....2..0..2..3....1..6..1..6

..3..2..3..2....3..2..8.13....0..5..0..5....0..2..8..2....4..1..4..1

Face neighbors:

0 -> 1 2 5

1 -> 0 4 6

2 -> 0 3 8

3 -> 2 4 16

4 -> 3 1 17

5 -> 0 7 9

6 -> 1 7 10

7 -> 6 5 11

8 -> 2 9 13

9 -> 8 5 14

10 -> 6 12 17

11 -> 7 12 14

12 -> 11 10 19

13 -> 8 15 16

14 -> 9 11 15

15 -> 14 13 19

16 -> 3 13 18

17 -> 4 10 18

18 -> 16 17 19

19 -> 15 18 12

CROSSREFS

Column 1 is A000244(n-1)

Column 2 is A005053

Sequence in context: A122847 A197462 A264098 * A233026 A105423 A147471

Adjacent sequences:  A223206 A223207 A223208 * A223210 A223211 A223212

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 18 2013

STATUS

approved

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Last modified May 27 13:04 EDT 2022. Contains 354097 sequences. (Running on oeis4.)