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%I #20 Apr 19 2019 11:45:41
%S 0,0,0,3,12,36,99,264,696,1827,4788,12540,32835,85968,225072,589251,
%T 1542684,4038804,10573731,27682392,72473448,189737955,496740420,
%U 1300483308,3404709507,8913645216,23336226144,61095033219,159948873516,418751587332,1096305888483
%N Number of vertices of type B at level n of the hyperbolic Pascal pyramid.
%H Colin Barker, <a href="/A292291/b292291.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 (2nd line of Table 1).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).
%F a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3), n >= 4.
%F G.f.: 3*x^3 / ((1 - x)*(1 - 3*x + x^2)). - _Colin Barker_, Sep 17 2017
%F a(n) = 3*Fibonacci(2*n - 3) - 3 for n > 0. - _Ehren Metcalfe_, Apr 18 2019
%t CoefficientList[Series[3*x^3/((1 - x)*(1 - 3*x + x^2)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 17 2017 *)
%t LinearRecurrence[{4,-4,1},{0,0,0,3},40] (* _Harvey P. Dale_, Oct 25 2017 *)
%o (PARI) concat(vector(3), Vec(3*x^3 / ((1 - x)*(1 - 3*x + x^2)) + O(x^40))) \\ _Colin Barker_, Sep 17 2017
%Y Cf. A264236.
%K nonn,easy
%O 0,4
%A _Eric M. Schmidt_, Sep 13 2017