A265058 - OEIS

%I #19 Feb 20 2024 16:06:50

%S 1,3,5,7,9,12,16,21,27,33,40,49,61,76,94,116,142,174,214,264,326,401,

%T 493,606,745,917,1129,1390,1710,2103,2587,3183,3917,4820,5931,7297,

%U 8977,11045,13590,16722,20575,25315,31147,38322,47151,58015,71382,87828,108062,132958,163590,201280,247654

%N Coordination sequence for (2,3,8) tiling of hyperbolic plane.

%H G. C. Greubel, <a href="/A265058/b265058.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, 0, 1, 0, 1, 0, 0, -1).

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

%t CoefficientList[Series[(x + 1)^2 (x^2 + x + 1) (x^6 + x^4 + x^2 + 1)/(x^10 - x^7 - x^5 - x^3 + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)

%o (PARI) x='x+O('x^50); Vec((x+1)^2*(x^2+x+1)*(x^6+x^4+x^2+1)/(x^10-x^7-x^5-x^3+1)) \\ _G. C. Greubel_, Aug 06 2017

%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