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%I #28 Jan 10 2018 03:24:36
%S 1,2,3,4,5,7,10,13,18,25,34,46,64,85,117,163,217,298,415,553,759,1057,
%T 1408,1933,2692,3586,4923,6856,9133,12538,17461,23260,31932,44470,
%U 59239,81325,113257,150871,207120,288445,384241
%N Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,132,e).
%H 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:1509.05239 [math.CO], 2015-2017. See Conjecture 5.8.
%F Conjectures from _Lars Blomberg_, Jan 08 2018: (Start)
%F n mod 3 == 0: a(n)=a(n-1)+a(n-4) for n>5.
%F n mod 3 == 1: a(n)=a(n-1)+a(n-4)-a(n-10) for n>9.
%F n mod 3 == 2: a(n)=a(n-1)+a(n-4)-a(n-14)-a(n-21) for n>22.
%F (End)
%F Conjectures from _Colin Barker_, Jan 09 2018: (Start)
%F G.f.: (1 + 2*x + 3*x^2 + 2*x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^10 - x^13) / (1 - 2*x^3 - x^6 - x^9).
%F a(n) = 2*a(n-3) + a(n-6) + a(n-9) for n>8.
%F (End)
%p A271489T := proc(n)
%p option remember;
%p local an,nrecur ;
%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(3,an),op(1,an)+op(3,an),op(2,an)] ;
%p else
%p # apply F1
%p [op(1,an),op(2,an),op(1,an)+op(3,an)] ;
%p end if;
%p end if;
%p end proc;
%p A271489 := 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(A271489T(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[[3]], an[[1]] + an[[3]], an[[2]]}, {an[[1]], an[[2]], an[[1]] + an[[3]]}]]];
%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, 20}] (* _Jean-François 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(11)-a(20) b _R. J. Mathar_, Apr 16 2016
%E a(21)-a(40) from _Lars Blomberg_, Jan 08 2018
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