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A063759
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Spherical growth series for modular group.
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9
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1, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Also number of sequences S of length n with entries in {1,..,q} where q = 3, satisfying the condition that adjacent terms differ in absolute value by exactly 1, see examples. - W. Edwin Clark, Oct 17 2008
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REFERENCES
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P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 156.
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LINKS
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FORMULA
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G.f.: (1+3*x+2*x^2)/(1-2*x^2).
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EXAMPLE
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For n = 2 the a(2) = 4 sequences are (1,2),(2,1),(2,3),(3,2). - W. Edwin Clark, Oct 17 2008
There are a(6) = 16 such words of length 6:
[ 1] [ 1 2 1 2 1 2 ]
[ 2] [ 1 2 1 2 3 2 ]
[ 3] [ 1 2 3 2 1 2 ]
[ 4] [ 1 2 3 2 3 2 ]
[ 5] [ 2 1 2 1 2 1 ]
[ 6] [ 2 1 2 1 2 3 ]
[ 7] [ 2 1 2 3 2 1 ]
[ 8] [ 2 1 2 3 2 3 ]
[ 9] [ 2 3 2 1 2 1 ]
[10] [ 2 3 2 1 2 3 ]
[11] [ 2 3 2 3 2 1 ]
[12] [ 2 3 2 3 2 3 ]
[13] [ 3 2 1 2 1 2 ]
[14] [ 3 2 1 2 3 2 ]
[15] [ 3 2 3 2 1 2 ]
[16] [ 3 2 3 2 3 2 ]
(End)
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MATHEMATICA
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Join[{1}, Transpose[NestList[{Last[#], 2First[#]}&, {3, 4}, 40]][[1]]] (* Harvey P. Dale, Oct 22 2011 *)
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PROG
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(Haskell)
import Data.List (transpose)
a063759 n = a063759_list !! n
a063759_list = concat $ transpose [a151821_list, a007283_list]
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CROSSREFS
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The sequence (ternary strings) seems to be related to A029744 and A090989.
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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