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A271489 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,132,e). 5
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 (list; graph; refs; listen; history; text; internal format)
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-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: 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

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Last modified March 21 12:12 EDT 2019. Contains 321369 sequences. (Running on oeis4.)