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A265075 Coordination sequence for (3,4,4) tiling of hyperbolic plane.

%I A265075 #27 Feb 20 2024 16:48:56
%S A265075 1,3,6,11,18,29,46,73,116,183,290,459,726,1149,1818,2877,4552,7203,
%T A265075 11398,18035,28538,45157,71454,113065,178908,283095,447954,708819,
%U A265075 1121598,1774757,2808282,4443677,7031440,11126179,17605478,27857979,44080994,69751437,110370990,174645225,276349380,437280663,691929826
%N A265075 Coordination sequence for (3,4,4) tiling of hyperbolic plane.
%H A265075 G. C. Greubel, <a href="/A265075/b265075.txt">Table of n, a(n) for n = 0..1000</a>
%H A265075 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 A265075 M. O'Keeffe, <a href="https://doi.org/10.1524/zkri.1998.213.3.135">Coordination sequences for hyperbolic tilings</a>, Zeitschrift für Kristallographie, 213 (1998), 135-140 (see last table, row 6.8.8H).
%H A265075 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 2, 1, 0, -1).
%F A265075 G.f.: (x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-2*x^3-x^2+1).
%t A265075 CoefficientList[Series[(x^3 + x^2 + x + 1) (x^2 + x + 1) (x + 1)/(x^6 - x^4 - 2 x^3 - x^2 + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)
%o A265075 (PARI) x='x+O('x^50); Vec((x^3+x^2+x+1)*(x^2+x+1)*(x+1)/(x^6-x^4-2*x^3-x^2+1)) \\ _G. C. Greubel_, Aug 07 2017
%Y A265075 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 A265075 nonn,easy
%O A265075 0,2
%A A265075 _N. J. A. Sloane_, Dec 29 2015