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%I #24 Sep 08 2022 08:46:19
%S 0,0,0,0,24,324,3600,38148,398112,4132596,42818208,443356212,
%T 4589665248,47509091508,491769434400,5090291998452,52689326584800,
%U 545383755284532,5645229662006688,58433377222329972,604839778633231200,6260653947359090868,64803587809297981728
%N Sum of values of vertices of type D at level n of the hyperbolic Pascal pyramid.
%H Colin Barker, <a href="/A292298/b292298.txt">Table of n, a(n) for n = 0..987</a>
%H László Németh, <a href="http://arxiv.org/abs/1511.02067">Hyperbolic Pascal pyramid</a>, arXiv:1511.0267 [math.CO], 2015 (4th line of Table 2).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-99,226,-224,92,-12).
%F a(n) = 18*a(n-1) - 99*a(n-2) + 226*a(n-3) - 224*a(n-4) + 92*a(n-5) - 12*a(n-6), n >= 7.
%F G.f.: 12*x^4*(2 - 9*x + 12*x^2) / ((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)). - _Colin Barker_, Sep 17 2017
%t Join[{0}, LinearRecurrence[{18, -99, 226, -224, 92, -12}, {0, 0, 0, 24, 324, 3600}, 20] ] (* _Vincenzo Librandi_, Sep 17 2017 *)
%t CoefficientList[Series[12*x^4*(2 - 9*x + 12*x^2)/((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Sep 17 2017 *)
%o (Magma) I:=[0,0,0,0,24,324,3600]; [n le 7 select I[n] else 18*Self(n-1)-99*Self(n-2)+226*Self(n-3)-224*Self(n-4)+ 92*Self(n-5)-12*Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Sep 17 2017
%o (PARI) concat(vector(4), Vec(12*x^4*(2 - 9*x + 12*x^2) / ((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)) + O(x^30))) \\ _Colin Barker_, Sep 17 2017
%Y Cf. A264237.
%K nonn,easy
%O 0,5
%A _Eric M. Schmidt_, Sep 14 2017
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