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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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5
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 156.
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LINKS
| Index entries for sequences related to modular groups
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FORMULA
| 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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MATHEMATICA
| Join[{1, 3}, 2Fibonacci[Range[4, 40]]] (* From Harvey P. Dale, Jan 06 2012 *)
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CROSSREFS
| Essentially the same as A006355.
Sequence in context: A145131 A152009 A114324 * A130578 A107068 A033541
Adjacent sequences: A054883 A054884 A054885 * A054887 A054888 A054889
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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