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Search: id:A054886
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| A054886 |
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Layer counting sequence for hyperbolic tessellation by cuspidal triangles of angles (Pi/3,Pi/3,0) (this is the classical modular tessellation). |
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+0
6
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| 1, 3, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The layer sequence is the sequence of the cardinalities of the layers accumulating around a ( finite-sided ) polygon of the tessellation under successive side-reflections; see the illustration accompanying A054888.
Also spherical growth series for modular group.
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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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Index entries for sequences related to modular groups
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FORMULA
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G.f.: (1+2*x+2*x^2+x^3)/(1-x-x^2) = (x^2+x+1)*(1+x)/(1-x-x^2). a(n)=2*F(n) for n>2, with F(n) the n-th Fibonacci number (cf. A000045 )
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CROSSREFS
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Essentially the same as A006355.
Adjacent sequences: A054883 A054884 A054885 this_sequence A054887 A054888 A054889
Sequence in context: A145131 A152009 A114324 this_sequence A130578 A107068 A033541
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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