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%I #17 Feb 20 2024 16:05:48
%S 1,3,5,7,9,12,16,20,24,28,33,40,48,57,67,78,92,109,129,152,178,209,
%T 246,290,342,402,472,555,653,769,905,1064,1251,1471,1731,2037,2396,
%U 2818,3314,3898,4586,5395,6346,7464,8779,10327,12148,14290,16809,19771,23256,27356,32179,37852,44524,52372
%N Coordination sequence for (2,3,7) tiling of hyperbolic plane.
%H G. C. Greubel, <a href="/A265057/b265057.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 (-1, 0, 1, 1, 1, 1, 1, 0, -1, -1).
%F G.f.: (x^6+x^5+x^4+x^3+x^2+x+1)*(x^2+x+1)*(x+1)^2/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1).
%t CoefficientList[Series[(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) (x^2 + x + 1) (x + 1)^2/(x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)
%o (PARI) x='x+O('x^50); Vec((x^6+x^5+x^4+x^3+x^2+x+1)*(x^2+x+1)*(x+1)^2/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+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
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