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A271486 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,23). 8

%I

%S 1,2,3,4,6,8,11,16,22,30,43,60,82,113,162,224,306,435,610,836,1168,

%T 1637,2282,3120,4399,6131,8522,11812,16561,22933,31810,44468,62335,

%U 85639,119452,167281,233169,320747,449700,626513,872175

%N Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,23).

%H Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen, <a href="http://arxiv.org/abs/1509.05239">Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences</a>, arXiv:1509.05239 [math.CO], 2015.

%p A271486T := proc(n)

%p option remember;

%p local an ;

%p if n = 1 then

%p [1,1,1] ;

%p else

%p an := procname(floor(n/2)) ;

%p if type(n,'even') then

%p # apply F0

%p [op(1,an)+op(3,an),op(3,an),op(2,an)] ;

%p else

%p # apply F1

%p [op(1,an),op(1,an)+op(3,an),op(2,an)] ;

%p end if;

%p end if;

%p end proc:

%p A271486 := proc(n)

%p local a,l,nmax;

%p a := 0 ;

%p for l from 2^n to 2^(n+1)-1 do

%p nmax := max( op(A271486T(l)) );

%p a := max(a,nmax) ;

%p end do:

%p a ;

%p end proc: # _R. J. Mathar_, Apr 16 2016

%t 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[[1]] + an[[3]], an[[2]]}]]];

%t 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];

%t Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* _Jean-Fran├žois Alcover_, Nov 17 2017, after _R. J. Mathar_ *)

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

%K nonn,more

%O 0,2

%A _N. J. A. Sloane_, Apr 13 2016

%E a(20)-a(40) from _Lars Blomberg_, Jan 08 2018

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Last modified April 25 13:31 EDT 2019. Contains 322461 sequences. (Running on oeis4.)