A265065 - OEIS

%I #17 Oct 18 2022 14:46:09

%S 1,3,5,8,13,20,29,42,62,91,132,192,281,410,597,870,1269,1851,2698,

%T 3933,5735,8362,12191,17774,25915,37784,55088,80317,117102,170734,

%U 248927,362932,529151,771496,1124831,1639989,2391084,3486171,5082793,7410648,10804633,15753020,22967705,33486626,48823082,71183443,103784568

%N Coordination sequence for (2,5,6) tiling of hyperbolic plane.

%H G. C. Greubel, <a href="/A265065/b265065.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 (0,0,1,1,2,1,1,0,0,-1).

%F G.f.: (x+1)^2*(x^4+x^3+x^2+x+1)*(x^4+x^2+1)/(x^10-x^7-x^6-2*x^5-x^4-x^3+1).

%t CoefficientList[Series[(x + 1)^2 (x^4 + x^3 + x^2 + x + 1) (x^4 + x^2 + 1) / (x^10 - x^7 - x^6 - 2 x^5 - x^4 - x^3 + 1), {x, 0, 45}], x] (* _Vincenzo Librandi_, Jan 20 2016 *)

%t LinearRecurrence[{0,0,1,1,2,1,1,0,0,-1},{1,3,5,8,13,20,29,42,62,91,132},50] (* _Harvey P. Dale_, Jun 15 2022 *)

%o (PARI) Vec((x+1)^2*(x^4+x^3+x^2+x+1)*(x^4+x^2+1)/(x^10-x^7-x^6-2*x^5-x^4-x^3+1) + O(x^50)) \\ _Michel Marcus_, Jan 20 2016

%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