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%I #21 Feb 28 2019 11:50:59
%S 3,8,21,56,148,394,1044,2776,7364,19568,51936,137960,366256,972736,
%T 2582736,6858880,18212288,48363680,128423232,341027456,905565760,
%U 2404701952,6385502208,16956417664,45026632448,119565922304,317499868416,843103631360,2238811202560,5945037720064,15786698462208,41920680589312,111317928707072
%N Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,23).
%H Georg Fischer, <a href="/A278615/b278615.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 (2,4,-6).
%F G.f.: ( 3+2*x-7*x^2 ) / ( 1-2*x-4*x^2+6*x^3 ). - _R. J. Mathar_, Dec 02 2016
%F a(n) = A271893(n)+A271894(n)+A271895(n). - _R. J. Mathar_, Dec 02 2016
%p A278615T := proc(n)
%p option remember;
%p local an, nrecur ;
%p if n = 1 then
%p [1, 1, 1] ;
%p else
%p an := procname(floor(n/2)) ;
%p if type(n, 'even') then
%p # apply F0
%p [op(1, an)+ op(3, an),op(3, an), op(2, an)] ;
%p else
%p # apply F1
%p [op(1, an), op(1, an)+ op(3, an),op(2, an)] ;
%p end if;
%p end if;
%p end proc;
%p A278615 := proc(n)
%p local a, l;
%p a := 0 ;
%p for l from 2^n to 2^(n+1)-1 do
%p L := A278615T(l) ;
%p a := a+ L[1]+L[2]+L[3] ;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Dec 02 2016
%t LinearRecurrence[{2, 4, -6}, {3, 8, 21}, 20] (* _Jean-François Alcover_, Nov 22 2017, after _R. J. Mathar_'s g.f. *)
%Y Cf. A271893, A278612, A278613, A278614, A278616.
%K nonn
%O 0,1
%A _Ilya Amburg_, Nov 23 2016
%E More terms from _R. J. Mathar_, Dec 02 2016
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