A271489 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,132,e).

1, 2, 3, 4, 5, 7, 10, 13, 18, 25, 34, 46, 64, 85, 117, 163, 217, 298, 415, 553, 759, 1057, 1408, 1933, 2692, 3586, 4923, 6856, 9133, 12538, 17461, 23260, 31932, 44470, 59239, 81325, 113257, 150871, 207120, 288445, 384241

Offset

0,2

Links

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

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], 2015-2017. See Conjecture 5.8.

Formula

Conjectures from Lars Blomberg, Jan 08 2018: (Start)

n mod 3 == 0: a(n)=a(n-1)+a(n-4) for n>5.

n mod 3 == 1: a(n)=a(n-1)+a(n-4)-a(n-10) for n>9.

n mod 3 == 2: a(n)=a(n-1)+a(n-4)-a(n-14)-a(n-21) for n>22.

(End)

Conjectures from Colin Barker, Jan 09 2018: (Start)

G.f.: (1 + 2*x + 3*x^2 + 2*x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^10 - x^13) / (1 - 2*x^3 - x^6 - x^9).

a(n) = 2*a(n-3) + a(n-6) + a(n-9) for n>8.

(End)

Maple

A271489T := 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(1, 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;
A271489 := proc(n)
    local a, l, nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271489T(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[[3]], an[[1]] + 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, 20}] (* 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: A174578 A241733 A241338 * A018127 A017835 A007601

Adjacent sequences: A271486 A271487 A271488 * A271490 A271491 A271492

Keyword

nonn,more

Author

N. J. A. Sloane, Apr 13 2016

Extensions

a(11)-a(20) b R. J. Mathar, Apr 16 2016

a(21)-a(40) from Lars Blomberg, Jan 08 2018

Status

approved