A271485 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e).

1, 2, 3, 5, 7, 11, 16, 25, 36, 56, 81, 126, 182, 283, 409, 636, 919, 1429, 2065, 3211, 4640, 7215, 10426, 16212, 23427, 36428, 52640, 81853, 118281, 183922, 265775, 413269, 597191, 928607, 1341876, 2086561, 3015168, 4688460, 6775021, 10534874, 15223334

Offset

0,2

Links

Table of n, a(n) for n=0..40.

Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 2015. See Conjecture 5.8.

Formula

Conjectures from Colin Barker, Apr 16 2016: (Start)

a(n) = 2*a(n-2)+a(n-4)-a(n-6) for n>5.

G.f.: (1+x)*(1+x-x^2)*(1+x^2) / (1-2*x^2-x^4+x^6).

(End)

Maple

A271485T := proc(n)
    option remember;
    local an ;
    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(1, an), op(2, an), op(1, an)+op(3, an)] ;
        end if;
    end if;
end proc:
A271485 := proc(n)
    local a, l, nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271485T(l)) );
        a := max(a, nmax) ;
    end do:
    a ;
end proc: # R. J. Mathar, Apr 16 2016

Mathematica

A271487T[n_] := A271487T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[1]] + an[[3]], an[[3]], an[[2]]}, {an[[1]], an[[2]], an[[1]] + an[[3]]}]]];
a[n_] := a[n] = Module[{a = 0, l, nMax}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, nMax = Max[A271487T[l]]; a = Max[a, nMax]]; a];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *)

Crossrefs

For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.

Sequence in context: A333588 A117792 A154888 * A018057 A355907 A130137

Adjacent sequences: A271482 A271483 A271484 * A271486 A271487 A271488

Keyword

nonn,more

Author

N. J. A. Sloane, Apr 13 2016

Extensions

a(20)-a(40) from Lars Blomberg, Jan 08 2018

Status

approved