A265062 - OEIS

%I #15 May 17 2023 16:15:17

%S 1,3,5,8,12,17,25,36,50,70,98,137,193,271,379,531,744,1042,1461,2048,

%T 2869,4020,5633,7893,11061,15500,21719,30434,42646,59758,83738,117340,

%U 164424,230402,322855,452406,633943,888325,1244781,1744272,2444193,3424970,4799303,6725112,9423686,13205113,18503907,25928939,36333403

%N Coordination sequence for (2,4,7) tiling of hyperbolic plane.

%H G. C. Greubel, <a href="/A265062/b265062.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 (0,0,1,1,1,1,1,0,0,-1).

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

%t CoefficientList[Series[(x + 1)^2 (x^2 + 1) (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^10 - x^7 - x^6 - x^5 - x^4 - x^3 + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 31 2015 *)

%t LinearRecurrence[{0,0,1,1,1,1,1,0,0,-1},{1,3,5,8,12,17,25,36,50,70,98},50] (* _Harvey P. Dale_, May 17 2023 *)

%o (PARI) Vec((x+1)^2*(x^2+1)*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^10-x^7-x^6-x^5-x^4-x^3+1) + O(x^50)) \\ _Michel Marcus_, Dec 31 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

%O 0,2

%A _N. J. A. Sloane_, Dec 29 2015