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%I #7 Apr 16 2016 13:15:40
%S 1,3,8,22,58,156,412,1100,2912,7752,20552,54640,144976,385200,1022464,
%T 2715872,7210400,19149504,50845376,135026368,358537216,952107648,
%U 2528205952,6713619200,17827416320,47340073728,125708097536,333811992064,886415931904,2353831246848,6250454268928,16597737933824
%N Expansion of (2*x+1)*(1-x) / ( 1-2*x-4*x^2+6*x^3 ).
%C Sum of all first elements at level n of the TRIP-Stern sequence corresponding to the permutation triple (e,13,23)
%H Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen, <a href="http://arxiv.org/abs/1509.05239">Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences</a>, arXiv:1509.05239 [math.CO], 2015, Section 7.2.1
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-6).
%F a(n) >= 2^n.
%o (PARI) x='x+O('x^99); Vec((2*x+1)*(1-x)/(1-2*x-4*x^2+6*x^3)) \\ _Altug Alkan_, Apr 16 2016
%Y Cf. A271486 (maximum at level n).
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Apr 16 2016
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