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A265077 Coordination sequence for (3,6,8) tiling of hyperbolic plane.

%I A265077 #26 Mar 06 2023 10:18:15
%S A265077 1,3,6,11,20,37,66,117,208,371,662,1179,2100,3741,6666,11877,21160,
%T A265077 37699,67166,119667,213204,379853,676762,1205749,2148216,3827355,
%U A265077 6818982,12148995,21645180,38563997,68707298,122411917,218094408,388566507,692287030,1233408755,2197494812,3915152565,6975406506,12427688349
%N A265077 Coordination sequence for (3,6,8) tiling of hyperbolic plane.
%H A265077 G. C. Greubel, <a href="/A265077/b265077.txt">Table of n, a(n) for n = 0..1000</a>
%H A265077 J. W. Cannon and 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 A265077 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,1,-1).
%F A265077 G.f.: (x^5+x^4+x^3+x^2+x+1)*(x+1)/(x^6-x^5-x^4-x^2-x+1).
%F A265077 a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5)-a(n-6) for n>6. - _Vincenzo Librandi_, Dec 30 2015
%t A265077 CoefficientList[Series[(x^5 + x^4 + x^3 + x^2 + x + 1) (x + 1)/(x^6 - x^5 - x^4 - x^2 - x + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)
%o A265077 (PARI) Vec((x^5+x^4+x^3+x^2+x+1)*(x+1)/(x^6-x^5-x^4-x^2-x+1) + O(x^50)) \\ _Michel Marcus_, Dec 30 2015
%o A265077 (Magma) I:=[1,3,6,11,20,37,66]; [n le 7 select I[n] else Self(n-1)+Self(n-2)+Self(n-4) + Self(n-5)-Self(n-6): n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2015
%Y A265077 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 A265077 nonn,easy
%O A265077 0,2
%A A265077 _N. J. A. Sloane_, Dec 29 2015