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A271487 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,132).

%I A271487 #21 Jan 08 2018 09:34:23
%S A271487 1,2,3,4,6,8,11,17,23,32,48,65,90,136,184,255,385,521,722,1090,1475,
%T A271487 2044,3086,4176,5787,8737,11823,16384,24736,33473,46386,70032,94768,
%U A271487 131327,198273,268305,371810,561346,759619,1052660,1589270
%N A271487 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,132).
%H A271487 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.
%F A271487 Conjectures from _Colin Barker_, Apr 16 2016: (Start)
%F A271487 a(n) = 2*a(n-3)+2*a(n-6)+a(n-9) for n>9.
%F A271487 G.f.: (1+x)*(1+x+2*x^2+2*x^4+x^6+x^8) / (1-2*x^3-2*x^6-x^9).
%F A271487 (End)
%p A271487 A271487T := proc(n)
%p A271487     option remember;
%p A271487     local an ;
%p A271487     if n = 1 then
%p A271487         [1,1,1] ;
%p A271487     else
%p A271487         an := procname(floor(n/2)) ;
%p A271487         if type(n,'even') then
%p A271487             # apply F0
%p A271487             [op(1,an)+op(3,an),op(3,an),op(2,an)] ;
%p A271487         else
%p A271487             # apply F1
%p A271487             [op(2,an),op(1,an)+op(3,an),op(1,an)] ;
%p A271487         end if;
%p A271487     end if;
%p A271487 end proc;
%p A271487 A271487 := proc(n)
%p A271487     local a,l,nmax;
%p A271487     a := 0 ;
%p A271487     for l from 2^n to 2^(n+1)-1 do
%p A271487         nmax := max( op(A271487T(l)) );
%p A271487         a := max(a,nmax) ;
%p A271487     end do:
%p A271487     a ;
%p A271487 end proc: # _R. J. Mathar_, Apr 16 2016
%t A271487 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[[2]], an[[1]] + an[[3]], an[[1]]}]]];
%t A271487 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 A271487 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 24}] (* _Jean-François Alcover_, Nov 17 2017, after _R. J. Mathar_ *)
%Y A271487 For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.
%K A271487 nonn,more
%O A271487 0,2
%A A271487 _N. J. A. Sloane_, Apr 13 2016
%E A271487 More terms from _Jean-François Alcover_, Nov 17 2017
%E A271487 a(25)-a(40) from _Lars Blomberg_, Jan 08 2018