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

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, A278614, A278615.

Programs

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 *)

Formula

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

Extensions

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