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A265070 Coordination sequence for (2,6,infinity) tiling of hyperbolic plane.

%I A265070 #20 Sep 08 2022 08:46:14
%S A265070 1,3,5,8,13,21,33,51,80,126,198,311,488,766,1203,1889,2966,4657,7312,
%T A265070 11481,18027,28305,44443,69782,109568,172038,270125,424136,665956,
%U A265070 1045649,1641823,2577904,4047689,6355468,9979021,15668533,24601905,38628615,60652616,95233542,149530690,234785211,368647368,578830674
%N A265070 Coordination sequence for (2,6,infinity) tiling of hyperbolic plane.
%H A265070 G. C. Greubel, <a href="/A265070/b265070.txt">Table of n, a(n) for n = 0..1000</a>
%H A265070 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 A265070 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,1).
%F A265070 G.f.: -(x^5+x^4+x^3+x^2+x+1)*(x+1)/(x^5+x^3+x-1).
%F A265070 a(n) = a(n-1)+a(n-3)+a(n-5) for n>6. - _Vincenzo Librandi_, Dec 30 2015
%t A265070 CoefficientList[Series[-(x^5 + x^4 + x^3 + x^2 + x + 1) (x + 1)/(x^5 + x^3 + x - 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)
%o A265070 (Magma) I:=[1,3,5,8,13,21,33]; [n le 7 select I[n] else Self(n-1)+Self(n-3)+Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2015
%o A265070 (PARI) x='x+O('x^50); Vec((x+1)*(x^5+x^4+x^3+x^2+x+1)/(1-x-x^3-x^5)) \\ _G. C. Greubel_, Aug 07 2017
%Y A265070 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 A265070 nonn,easy
%O A265070 0,2
%A A265070 _N. J. A. Sloane_, Dec 29 2015