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%I #17 Sep 08 2022 08:46:14
%S 1,3,6,10,16,26,42,67,106,167,264,418,662,1048,1658,2623,4150,6567,
%T 10392,16444,26020,41172,65148,103087,163120,258113,408424,646268,
%U 1022620,1618140,2560460,4051537,6410938,10144329,16051850,25399600,40190986,63596094,100631100,159233337,251962422,398692029,630869210
%N Coordination sequence for (3,3,7) tiling of hyperbolic plane.
%H G. C. Greubel, <a href="/A265074/b265074.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 (1,0,1,0,1,0,1,-1).
%F G.f.: (x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^8-x^7-x^5-x^3-x+1).
%F a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)-a(n-8) for n>8. - _Vincenzo Librandi_, Dec 30 2015
%t CoefficientList[Series[(x^2 + x + 1) (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/(x^8 - x^7 - x^5 - x^3 - x + 1), {x, 0, 60}], x] (* _Vincenzo Librandi_, Dec 30 2015 *)
%o (Magma) I:=[1,3,6,10,16,26,42,67,106]; [n le 9 select I[n] else Self(n-1)+Self(n-3)+Self(n-5)+Self(n-7)-Self(n-8): n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2015
%o (PARI) x='x+O('x^50); Vec((x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^8-x^7-x^5-x^3-x+1)) \\ _G. C. Greubel_, Aug 07 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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