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A189673
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Fixed point of the morphism 0->010, 1->110.
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3
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0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1
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OFFSET
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1
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COMMENTS
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A generalized choral sequence c(3n+r_0)=0, c(3n+r_1)=1, c(3n+r_c)=c(n), with r_0=2, r_1=1, r_c=0, and c(0)=0. - Joel Reyes Noche, Jun 14 2021
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REFERENCES
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Joel Reyes Noche, Generalized Choral Sequences, Matimyas Matematika, 31(2008), 25-28.
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LINKS
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FORMULA
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a(3k-2)=a(k), a(3k-1)=1, a(3k)=0 for k>=1, a(0)=0.
G.f. satisfies g(x) = x^2/(1-x^3) + g(x^3)/x^2. - Robert Israel, Feb 15 2017
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EXAMPLE
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0->010->010110010->
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MAPLE
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f:= proc(n) option remember;
if n mod 3 = 1 then procname((n+2)/3) else -n mod 3 fi;
end proc:
f(1):= 0:
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MATHEMATICA
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t = Nest[Flatten[# /. {0->{0, 1, 0}, 1->{1, 1, 0}}] &, {0}, 5] (*A189673*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A026227 conjectured *)
Flatten[Position[t, 1]] (* A026138 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189674*)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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