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A278616 Sum of terms in level n of TRIP -  Stern sequence associated with permutation triple (e,13,132). 5
3, 8, 21, 56, 148, 393, 1041, 2761, 7318, 19403, 51436, 136366, 361513, 958413, 2540831, 6735996, 17857733, 47342548, 125509476, 332737401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..19.

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.

FORMULA

Conjecture: G.f.: ( -3-5*x-x^2 ) / ( -1+x+4*x^2+x^3 ). - R. J. Mathar, Dec 02 2016

MAPLE

A278616T := 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(2, an), op(1, an)+ op(3, an), op(1, an)] ;

        end if;

    end if;

end proc;

A278616 := proc(n)

    local a, l;

    a := 0 ;

    for l from 2^n to 2^(n+1)-1 do

        L := A278616T(l) ;

        # a := a+ L[1]+L[2]+L[3] ;

        a := a+ L[2];

    end do:

    a ;

end proc: # R. J. Mathar, Dec 02 2016

MATHEMATICA

AT[n_] := AT[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = AT[Floor[n/2]]; If[EvenQ[n], {an[[1]] + an[[3]], an[[3]], an[[2]]}, {an[[2]], an[[1]] + an[[3]], an[[1]] } ]]];

a[n_] := a[n] = Module[{a = 0, l, L}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, L = AT[l]; a = a + L[[1]] + L[[2]] + L[[3]]]; a];

Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* Jean-Fran├žois Alcover, Nov 22 2017, after R. J. Mathar *)

CROSSREFS

Cf. A278612, A278613, A278614, A278615.

Sequence in context: A278613 A072632 A001671 * A278615 A090413 A128105

Adjacent sequences:  A278613 A278614 A278615 * A278617 A278618 A278619

KEYWORD

nonn,more

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 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)