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A271487
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Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,132).
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5
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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
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OFFSET
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0,2
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LINKS
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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.
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FORMULA
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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)
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MAPLE
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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;
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 ;
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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[[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];
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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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