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%I #16 Feb 20 2024 16:11:28
%S 1,3,5,8,12,17,25,37,53,75,107,152,216,309,441,628,895,1275,1816,2588,
%T 3689,5257,7491,10675,15211,21675,30888,44016,62723,89381,127368,
%U 181499,258637,368560,525200,748413,1066493,1519757,2165661,3086079,4397679,6266716,8930104,12725445,18133825,25840796,36823271,52473355
%N Coordination sequence for (2,4,8) tiling of hyperbolic plane.
%H G. C. Greubel, <a href="/A265063/b265063.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, -1, 1, 0, 1, -1).
%F G.f.: (x^2+1)*(x^4+1)*(x+1)^2/(x^8-x^7-x^5+x^4-x^3-x+1).
%t CoefficientList[Series[(x^2 + 1)*(x^4 + 1)*(x + 1)^2/(x^8 - x^7 - x^5 + x^4 - x^3 - x + 1), {x, 0, 50}], x] (* _G. C. Greubel_, Aug 07 2017 *)
%o (PARI) Vec((x^2+1)*(x^4+1)*(x+1)^2/(x^8-x^7-x^5+x^4-x^3-x+1) + O(x^100)) \\ _Altug Alkan_, Dec 29 2015
%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
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