%I #19 Jan 19 2019 04:12:32
%S 3,8,22,60,162,436,1174,3164,8530,22996,61990,167100,450434,1214196,
%T 3273014,8822812,23782962,64109844,172815814,465845884,1255743842,
%U 3385009204,9124701142,24596733916,66303466770,178729002068,481785610086,1298711297084,3500833146178,9436918539636,25438353615990
%N Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e, e, e).
%H Colin Barker, <a href="/A278612/b278612.txt">Table of n, a(n) for n = 0..1000</a>
%H I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, <a href="https://arxiv.org/abs/1509.05239">Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences</a>, arXiv:1509.05239 [math.CO], 17 Sep 2015.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,4).
%F a(n) = A271896(n) + A271897(n) + A271898(n). - _R. J. Mathar_, Dec 02 2016
%F From _Colin Barker_, Jan 09 2018: (Start)
%F G.f.: (3 - 4*x + 5*x^2) / (1 - 4*x + 5*x^2 - 4*x^3).
%F a(n) = 4*a(n-1) - 5*a(n-2) + 4*a(n-3) for n>2.
%F (End)
%o (PARI) Vec((3 - 4*x + 5*x^2) / (1 - 4*x + 5*x^2 - 4*x^3) + O(x^40)) \\ _Colin Barker_, Jan 09 2018
%Y Cf. A278613, A278614, A278615, A278616.
%K nonn,easy
%O 0,1
%A _Ilya Amburg_, Nov 23 2016