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A271485 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e). 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A112088 A117792 A154888 * A018057 A130137 A218022

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

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Last modified February 18 13:07 EST 2018. Contains 299322 sequences. (Running on oeis4.)