A278614 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,12,12).

3, 8, 22, 62, 176, 502, 1434, 4100, 11726, 33542, 95952, 274494, 785266, 2246484, 6426742, 18385646, 52597744, 150471910, 430470890, 1231493604

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

Maple

A278614T := 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(3, an), op(2, an), op(1, an)+ op(3, an)] ;
        else
            # apply F1
            [op(2, an), op(1, an), op(1, an)+op(3, an)] ;
        end if;
    end if;
end proc;
A278614 := proc(n)
    local a, l;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        L := A278614T(l) ;
        a := a+ L[1]+L[2]+L[3] ;
    end do:
    a ;
end proc: # R. J. Mathar, Dec 02 2016

Mathematica

A278614T[n_] := A278614T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[3]], an[[2]], an[[1]] + an[[3]]}, {an[[2]], an[[1]], an[[1]] + an[[3]]}]]];
a[n_] := a[n] = Module[{a = 0, l, L}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, L = A278614T[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 20 2017, after R. J. Mathar *)

Crossrefs

Cf. A278612, A278613, A278615, A278616.

Sequence in context: A018040 A018041 A073357 * A188464 A298260 A336990

Adjacent sequences: A278611 A278612 A278613 * A278615 A278616 A278617

Keyword

nonn,more

Author

Ilya Amburg, Nov 23 2016

Extensions

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

Status

approved