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Number of vertices of type D at level n of the hyperbolic Pascal pyramid.
1

%I #15 Sep 18 2017 08:03:36

%S 0,0,0,0,3,24,177,1347,10467,82029,644808,5073915,39939900,314427960,

%T 2475438408,19488960504,153435934587,1207997701872,9510543548457,

%U 74876345104299,589500202673403,4641125238026805,36539501601385200,287674887310843395,2264859596198883588

%N Number of vertices of type D at level n of the hyperbolic Pascal pyramid.

%H Colin Barker, <a href="/A292293/b292293.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 (4th 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.: 3*x^4*(1 - 4*x) / ((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)). - _Colin Barker_, Sep 17 2017

%t CoefficientList[Series[3*x^4*(1 - 4*x)/((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(4), Vec(3*x^4*(1 - 4*x) / ((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