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

%I A271486 #18 Jan 08 2018 09:34:05
%S A271486 1,2,3,4,6,8,11,16,22,30,43,60,82,113,162,224,306,435,610,836,1168,
%T A271486 1637,2282,3120,4399,6131,8522,11812,16561,22933,31810,44468,62335,
%U A271486 85639,119452,167281,233169,320747,449700,626513,872175
%N A271486 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,23).
%H A271486 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 A271486 A271486T := proc(n)
%p A271486     option remember;
%p A271486     local an ;
%p A271486     if n = 1 then
%p A271486         [1,1,1] ;
%p A271486     else
%p A271486         an := procname(floor(n/2)) ;
%p A271486         if type(n,'even') then
%p A271486             # apply F0
%p A271486             [op(1,an)+op(3,an),op(3,an),op(2,an)] ;
%p A271486         else
%p A271486             # apply F1
%p A271486             [op(1,an),op(1,an)+op(3,an),op(2,an)] ;
%p A271486         end if;
%p A271486     end if;
%p A271486 end proc:
%p A271486 A271486 := proc(n)
%p A271486     local a,l,nmax;
%p A271486     a := 0 ;
%p A271486     for l from 2^n to 2^(n+1)-1 do
%p A271486         nmax := max( op(A271486T(l)) );
%p A271486         a := max(a,nmax) ;
%p A271486     end do:
%p A271486     a ;
%p A271486 end proc: # _R. J. Mathar_, Apr 16 2016
%t A271486 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 A271486 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 A271486 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* _Jean-François Alcover_, Nov 17 2017, after _R. J. Mathar_ *)
%Y A271486 For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
%K A271486 nonn,more
%O A271486 0,2
%A A271486 _N. J. A. Sloane_, Apr 13 2016
%E A271486 a(20)-a(40) from _Lars Blomberg_, Jan 08 2018