|
%I #19 Feb 20 2024 16:07:51
%S 1,3,5,7,9,12,16,21,28,36,45,56,70,89,113,143,181,228,287,361,455,575,
%T 726,916,1155,1456,1836,2315,2920,3684,4647,5861,7391,9321,11756,
%U 14827,18701,23587,29749,37520,47320,59681,75272,94936,119737,151016,190466,240221,302973,382119,481941,607840,766627
%N Coordination sequence for (2,3,9) tiling of hyperbolic plane.
%H G. C. Greubel, <a href="/A265059/b265059.txt">Table of n, a(n) for n = 0..1000</a>
%H J. W. Cannon, P. Wagreich, <a href="http://dx.doi.org/10.1007/BF01444714">Growth functions of surface groups</a>, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 0, 1, 0, 0, 1, 0, -1).
%F G.f.: (x+1)^2*(x^2+x+1)*(x^6+x^3+1)/(x^10-x^8-x^5-x^2+1).
%t CoefficientList[Series[(x + 1)^2 (x^2 + x + 1) (x^6 + x^3 + 1)/(x^10 - x^8 - x^5 - x^2 + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)
%o (PARI) x='x+O('x^50); Vec((x+1)^2*(x^2+x+1)*(x^6+x^3+1)/(x^10-x^8-x^5-x^2+1)) \\ _G. C. Greubel_, Aug 06 2017
%Y 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.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 29 2015
|
