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A271488 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,23,e).

%I A271488 #27 Jan 08 2018 09:18:58
%S A271488 1,2,3,4,5,8,11,15,21,30,41,56,79,112,153,209,297,418,571,782,1109,
%T A271488 1560,2131,2940,4141,5822,7953,10981,15455,21728,29681,41003,57681,
%U A271488 81090,110771,153105,215269,302632,413403,571428,803397
%N A271488 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,23,e).
%H A271488 I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, <a href="http://arxiv.org/abs/1509.05239">Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences</a>, arXiv:1509.05239v1 [math.CO] 17 Sep 2015. See Conjecture 5.8.
%p A271488 A271488T := proc(n)
%p A271488     option remember;
%p A271488     local an ;
%p A271488     if n = 1 then
%p A271488         [1,1,1] ;
%p A271488     else
%p A271488         an := procname(floor(n/2)) ;
%p A271488         if type(n,'even') then
%p A271488             # apply F0
%p A271488             [op(2,an),op(1,an)+op(3,an),op(3,an)] ;
%p A271488         else
%p A271488             # apply F1
%p A271488             [op(1,an),op(2,an),op(1,an)+op(3,an)] ;
%p A271488         end if;
%p A271488     end if;
%p A271488 end proc:
%p A271488 A271488 := proc(n)
%p A271488     local a,l,nmax;
%p A271488     a := 0 ;
%p A271488     for l from 2^n to 2^(n+1)-1 do
%p A271488         nmax := max( op(A271488T(l)) );
%p A271488         a := max(a,nmax) ;
%p A271488     end do:
%p A271488     a ;
%p A271488 end proc: # _R. J. Mathar_, Apr 16 2016
%t A271488 A271487T[n_] := A271487T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[2]], an[[1]] + an[[3]], an[[3]]}, {an[[1]], an[[2]], an[[1]] + an[[3]]}]]];
%t A271488 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 A271488 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 20}] (* _Jean-François Alcover_, Nov 17 2017, after _R. J. Mathar_ *)
%Y A271488 For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
%K A271488 nonn,more
%O A271488 0,2
%A A271488 _N. J. A. Sloane_, Apr 13 2016
%E A271488 a(4) corrected by _Jean-François Alcover_ and _Vaclav Kotesovec_, Nov 18 2017
%E A271488 a(21)-a(24) from _Vaclav Kotesovec_, Nov 18 2017
%E A271488 a(25)-a(26) from _Vaclav Kotesovec_, Nov 29 2017
%E A271488 a(27)-a(40) from _Lars Blomberg_, Jan 08 2018