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A271485 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e).

%I A271485 #24 Jan 08 2018 09:20:29
%S A271485 1,2,3,5,7,11,16,25,36,56,81,126,182,283,409,636,919,1429,2065,3211,
%T A271485 4640,7215,10426,16212,23427,36428,52640,81853,118281,183922,265775,
%U A271485 413269,597191,928607,1341876,2086561,3015168,4688460,6775021,10534874,15223334
%N A271485 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e).
%H A271485 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. See Conjecture 5.8.
%F A271485 Conjectures from _Colin Barker_, Apr 16 2016: (Start)
%F A271485 a(n) = 2*a(n-2)+a(n-4)-a(n-6) for n>5.
%F A271485 G.f.: (1+x)*(1+x-x^2)*(1+x^2) / (1-2*x^2-x^4+x^6).
%F A271485 (End)
%p A271485 A271485T := proc(n)
%p A271485     option remember;
%p A271485     local an ;
%p A271485     if n = 1 then
%p A271485         [1,1,1] ;
%p A271485     else
%p A271485         an := procname(floor(n/2)) ;
%p A271485         if type(n,'even') then
%p A271485             # apply F0
%p A271485             [op(1,an)+op(3,an),op(3,an),op(2,an)] ;
%p A271485         else
%p A271485             # apply F1
%p A271485             [op(1,an),op(2,an),op(1,an)+op(3,an)] ;
%p A271485         end if;
%p A271485     end if;
%p A271485 end proc:
%p A271485 A271485 := proc(n)
%p A271485     local a,l,nmax;
%p A271485     a := 0 ;
%p A271485     for l from 2^n to 2^(n+1)-1 do
%p A271485         nmax := max( op(A271485T(l)) );
%p A271485         a := max(a,nmax) ;
%p A271485     end do:
%p A271485     a ;
%p A271485 end proc: # _R. J. Mathar_, Apr 16 2016
%t A271485 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]]}]]];
%t A271485 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 A271485 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* _Jean-François Alcover_, Nov 17 2017, after _R. J. Mathar_ *)
%Y A271485 For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
%K A271485 nonn,more
%O A271485 0,2
%A A271485 _N. J. A. Sloane_, Apr 13 2016
%E A271485 a(20)-a(40) from _Lars Blomberg_, Jan 08 2018