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

0,2

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:1509.05239v1 [math.CO] 17 Sep 2015. See Conjecture 5.8.

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)

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 *)

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: A281094 A054782 A261082 * A211397 A173542 A323383

Adjacent sequences: A271484 A271485 A271486 * A271488 A271489 A271490

Keyword

nonn,more

Author

N. J. A. Sloane, Apr 13 2016

Extensions

More terms from Jean-François Alcover, Nov 17 2017

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

Status

approved