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 A054886 Layer counting sequence for hyperbolic tessellation by cuspidal triangles of angles (Pi/3,Pi/3,0) (this is the classical modular tessellation). 33
 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; text; internal format)
 OFFSET 1,2 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. Equivalently, coordination sequence for (3,3,infinity) tiling of hyperbolic plane. - N. J. A. Sloane, Dec 29 2015 Equivalently, spherical growth series for modular group. REFERENCES P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 156. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1. 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 ) MATHEMATICA Join[{1, 3}, 2Fibonacci[Range[4, 40]]] (* Harvey P. Dale, Jan 06 2012 *) PROG (PARI) x='x+O('x^50); Vec((1+2*x+2*x^2+x^3)/(1-x-x^2)) \\ G. C. Greubel, Aug 06 2017 CROSSREFS Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077. Essentially the same as A006355. Sequence in context: A114324 A265073 A265074 * A130578 A107068 A033541 Adjacent sequences:  A054883 A054884 A054885 * A054887 A054888 A054889 KEYWORD nonn,easy,nice AUTHOR Paolo Dominici (pl.dm(AT)libero.it), May 23 2000 STATUS approved

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Last modified April 15 11:07 EDT 2021. Contains 342977 sequences. (Running on oeis4.)