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 A271487 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,132). 11
 1, 2, 3, 4, 6, 8, 11, 17, 23, 32, 48, 65, 90, 136, 184, 255, 385, 521, 722, 1090, 1475, 2044, 3086, 4176, 5787, 8737, 11823, 16384, 24736, 33473, 46386, 70032, 94768, 131327, 198273, 268305, 371810, 561346, 759619, 1052660, 1589270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239v1 [math.CO] 17 Sep 2015. See Conjecture 5.8. FORMULA Conjectures from Colin Barker, Apr 16 2016: (Start) a(n) = 2*a(n-3)+2*a(n-6)+a(n-9) for n>9. 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). (End) MAPLE A271487T := 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(2, an), op(1, an)+op(3, an), op(1, an)] ;         end if;     end if; end proc; A271487 := proc(n)     local a, l, nmax;     a := 0 ;     for l from 2^n to 2^(n+1)-1 do         nmax := max( op(A271487T(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[[2]], an[[1]] + an[[3]], an[[1]]}]]]; 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, 24}] (* 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: A281094 A054782 A261082 * A211397 A173542 A323383 Adjacent sequences:  A271484 A271485 A271486 * A271488 A271489 A271490 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Apr 13 2016 EXTENSIONS More terms from Jean-François Alcover, Nov 17 2017 a(25)-a(40) from Lars Blomberg, Jan 08 2018 STATUS approved

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Last modified December 6 14:47 EST 2019. Contains 329806 sequences. (Running on oeis4.)