A278615 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,23).

3, 8, 21, 56, 148, 394, 1044, 2776, 7364, 19568, 51936, 137960, 366256, 972736, 2582736, 6858880, 18212288, 48363680, 128423232, 341027456, 905565760, 2404701952, 6385502208, 16956417664, 45026632448, 119565922304, 317499868416, 843103631360, 2238811202560, 5945037720064, 15786698462208, 41920680589312, 111317928707072

Offset

0,1

Links

Georg Fischer, Table of n, a(n) for n = 0..1000

I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 17 Sep 2015.

Index entries for linear recurrences with constant coefficients, signature (2,4,-6).

Formula

G.f.: ( 3+2*x-7*x^2 ) / ( 1-2*x-4*x^2+6*x^3 ). - R. J. Mathar, Dec 02 2016

a(n) = A271893(n)+A271894(n)+A271895(n). - R. J. Mathar, Dec 02 2016

Maple

A278615T := proc(n)
    option remember;
    local an, nrecur ;
    if n = 1 then
        [1, 1, 1] ;
    else
        an := procname(floor(n/2)) ;
        if type(n, 'even') then
            # apply F0
            [op(1, an)+ op(3, an), op(3, an), op(2, an)] ;
        else
            # apply F1
            [op(1, an), op(1, an)+ op(3, an), op(2, an)] ;
        end if;
    end if;
end proc;
A278615 := proc(n)
    local a, l;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        L := A278615T(l) ;
        a := a+ L[1]+L[2]+L[3] ;
    end do:
    a ;
end proc: # R. J. Mathar, Dec 02 2016

Mathematica

LinearRecurrence[{2, 4, -6}, {3, 8, 21}, 20] (* Jean-François Alcover, Nov 22 2017, after R. J. Mathar's g.f. *)

Crossrefs

Cf. A271893, A278612, A278613, A278614, A278616.

Sequence in context: A360054 A309226 A278616 * A090413 A128105 A085560

Adjacent sequences: A278612 A278613 A278614 * A278616 A278617 A278618

Keyword

nonn

Author

Ilya Amburg, Nov 23 2016

Extensions

More terms from R. J. Mathar, Dec 02 2016

Status

approved