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A278615 Sum of terms in level n of TRIP -  Stern sequence associated with permutation triple (e,13,23). 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 22 2017, after R. J. Mathar's g.f. *)

CROSSREFS

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

Sequence in context: A072632 A001671 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

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Last modified March 26 20:47 EDT 2019. Contains 321535 sequences. (Running on oeis4.)