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 A271485 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e). 5
 1, 2, 3, 5, 7, 11, 16, 25, 36, 56, 81, 126, 182, 283, 409, 636, 919, 1429, 2065, 3211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 2015. See Conjecture 5.8. FORMULA Conjectures from Colin Barker, Apr 16 2016: (Start) a(n) = 2*a(n-2)+a(n-4)-a(n-6) for n>5. G.f.: (1+x)*(1+x-x^2)*(1+x^2) / (1-2*x^2-x^4+x^6). (End) MAPLE A271485T := proc(n)     option remember;     local an ;     if n = 1 then         [1, 1, 1] ;     else         an := procname(floor(n/2)) ;         if type(n, 'even') then             # apply F0             [op(1, an)+op(3, an), op(3, an), op(2, an)] ;         else             # apply F1             [op(1, an), op(2, an), op(1, an)+op(3, an)] ;         end if;     end if; end proc: A271485 := proc(n)     local a, l, nmax;     a := 0 ;     for l from 2^n to 2^(n+1)-1 do         nmax := max( op(A271485T(l)) );         a := max(a, nmax) ;     end do:     a ; end proc: # R. J. Mathar, Apr 16 2016 MATHEMATICA 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]]}]]]; 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]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *) CROSSREFS For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489. Sequence in context: A112088 A117792 A154888 * A018057 A130137 A218022 Adjacent sequences:  A271482 A271483 A271484 * A271486 A271487 A271488 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Apr 13 2016 STATUS approved

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