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%I #19 May 26 2019 15:08:01
%S 0,0,0,1,3,9,34,174,1128,8251,63315,494175,3879370,30512736,240149088,
%T 1890487729,14883249459,117174190329,922506823618,7262871367566,
%U 57180440473320,450180590519275,3544264121625315,27903931958216271,219687190433359498
%N Number of vertices of type C at level n of the hyperbolic Pascal pyramid.
%H Colin Barker, <a href="/A292292/b292292.txt">Table of n, a(n) for n = 0..1000</a>
%H László Németh, <a href="http://arxiv.org/abs/1511.02067">Hyperbolic Pascal pyramid</a>, arXiv:1511.0267 [math.CO], 2015 (3rd line of Table 1).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (12,-37,37,-12,1).
%F a(n) = 12*a(n-1) - 37*a(n-2) + 37*a(n-3) - 12*a(n-4) + a(n-5), n >= 6.
%F G.f.: x^3*(1 - 9*x + 10*x^2) / ((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)). - _Colin Barker_, Sep 17 2017
%F a(n) = A001091(n-3)/15 + 3*A002878(n-3)/5 + 1/3 for n > 0. - _Ehren Metcalfe_, Apr 18 2019
%t CoefficientList[Series[x^3*(1 - 9*x + 10*x^2)/((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 17 2017 *)
%o (PARI) concat(vector(3), Vec(x^3*(1 - 9*x + 10*x^2) / ((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)) + O(x^30))) \\ _Colin Barker_, Sep 17 2017
%Y Cf. A264236.
%K nonn,easy
%O 0,5
%A _Eric M. Schmidt_, Sep 13 2017
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