A271487 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,132).

1, 2, 3, 4, 6, 8, 11, 17, 23, 32, 48, 65, 90, 136, 184, 255, 385, 521, 722, 1090, 1475, 2044, 3086, 4176, 5787, 8737, 11823, 16384, 24736, 33473, 46386, 70032, 94768, 131327, 198273, 268305, 371810, 561346, 759619, 1052660, 1589270

Offset: 0

Author

N. J. A. Sloane, Apr 13 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:1509.05239v1 [math.CO] 17 Sep 2015. See Conjecture 5.8.

Crossrefs

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

Programs

Maple

A271487T := 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(2,an),op(1,an)+op(3,an),op(1,an)] ;
        end if;
    end if;
end proc;
A271487 := proc(n)
    local a,l,nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271487T(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[[2]], an[[1]] + an[[3]], an[[1]]}]]];
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, 24}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *)

Formula

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

a(n) = 2*a(n-3)+2*a(n-6)+a(n-9) for n>9.

G.f.: (1+x)*(1+x+2*x^2+2*x^4+x^6+x^8) / (1-2*x^3-2*x^6-x^9).

(End)

Extensions

More terms from Jean-François Alcover, Nov 17 2017

a(25)-a(40) from Lars Blomberg, Jan 08 2018