A278616 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,132).

3, 8, 21, 56, 148, 393, 1041, 2761, 7318, 19403, 51436, 136366, 361513, 958413, 2540831, 6735996, 17857733, 47342548, 125509476, 332737401

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-François Alcover, Nov 22 2017, after R. J. Mathar *)

Crossrefs

Cf. A278612, A278613, A278614, A278615.

Sequence in context: A001671 A360054 A309226 * 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