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A271485
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Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e).
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5
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1, 2, 3, 5, 7, 11, 16, 25, 36, 56, 81, 126, 182, 283, 409, 636, 919, 1429, 2065, 3211, 4640, 7215, 10426, 16212, 23427, 36428, 52640, 81853, 118281, 183922, 265775, 413269, 597191, 928607, 1341876, 2086561, 3015168, 4688460, 6775021, 10534874, 15223334
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OFFSET
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0,2
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LINKS
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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.
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FORMULA
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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)
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MAPLE
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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:
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 ;
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MATHEMATICA
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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];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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