A265061 - OEIS

%I #22 Feb 20 2024 16:09:41

%S 1,3,5,8,12,17,24,33,45,61,83,114,155,210,286,389,529,720,979,1331,

%T 1810,2462,3349,4554,6193,8423,11455,15579,21188,28815,39188,53296,

%U 72483,98577,134064,182327,247965,337232,458636,623745,848292,1153677,1569001,2133841,2902023,3946750,5367579,7299906,9927870,13501901

%N Coordination sequence for (2,4,6) tiling of hyperbolic plane.

%H G. C. Greubel, <a href="/A265061/b265061.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, -1, 2, -1, 2, -1, 1, -1).

%F G.f.: (x+1)^2*(x^2+1)*(x^4+x^2+1)/(x^8-x^7+x^6-2*x^5+x^4-2*x^3+x^2-x+1).

%t CoefficientList[Series[(x + 1)^2 (x^2 + 1) (x^4 + x^2 + 1)/(x^8 - x^7 + x^6 - 2 x^5 + x^4 - 2 x^3 + x^2 - x + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)

%o (PARI) Vec((x+1)^2*(x^2+1)*(x^4+x^2+1)/(x^8-x^7+x^6-2*x^5+x^4-2*x^3+x^2-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