cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A265067 Coordination sequence for (2,5,8) tiling of hyperbolic plane.

This page as a plain text file.
%I A265067 #17 Feb 22 2025 22:31:40
%S A265067 1,3,5,8,13,20,30,46,70,105,158,238,358,539,813,1225,1844,2777,4183,
%T A265067 6300,9488,14291,21525,32419,48827,73540,110761,166821,251256,378426,
%U A265067 569960,858437,1292923,1947317,2932923,4417381,6653176,10020585,15092360,22731142,34236184,51564338,77662890,116970850,176173970,265341902
%N A265067 Coordination sequence for (2,5,8) tiling of hyperbolic plane.
%H A265067 G. C. Greubel, <a href="/A265067/b265067.txt">Table of n, a(n) for n = 0..1000</a>
%H A265067 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 A265067 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 0, -1).
%F A265067 G.f.: (x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^4+x^2+1)/(x^12-x^9-x^8-2*x^7-x^6-2*x^5-x^4-x^3+1).
%t A265067 CoefficientList[Series[(x + 1)^2 (x^4 + x^3 + x^2 + x + 1) (x^6 + x^4 + x^2 + 1) / (x^12 - x^9 - x^8 - 2 x^7 - x^6 - 2 x^5 - x^4 - x^3 + 1), {x, 0, 45}], x] (* _Vincenzo Librandi_, Jan 20 2016 *)
%o A265067 (PARI) Vec((x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^4+x^2+1)/(x^12-x^9-x^8-2*x^7-x^6-2*x^5-x^4-x^3+1) + O(x^50)) \\ _Michel Marcus_, Jan 20 2016
%Y A265067 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 A265067 nonn,easy
%O A265067 0,2
%A A265067 _N. J. A. Sloane_, Dec 29 2015