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

Author

Ilya Amburg, Nov 23 2016

Keywords

• nonn
• more

Links

• 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.

Crossrefs

Cf. A278612, A278613, A278615, A278616.

Programs

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 *)

Formula

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

Extensions

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