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0, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 3, 4, 5, 5, 4, 5, 7, 8, 7, 7, 8, 7, 5, 4, 5, 5, 4, 3, 3, 2, 1, 1, 2, 3, 3, 4, 5, 5, 4, 5, 7, 8, 7, 7, 8, 7, 5, 6, 9, 11, 10, 11, 13, 12, 9, 9, 12, 13, 11, 10, 11, 9, 6
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OFFSET
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1,4
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COMMENTS
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a(n)/A287731(n) enumerates all reduced fractions along the Stern-Brocot Tree. See the Serov link below.
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LINKS
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FORMULA
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Consider for n > 1 the binary expansion b(1:t) of n-1 without the leading 1.
Recurse: c=s=1; for j=1:t {if b(t-j+1) == mod(t,2) s = s+c; else c = c+s;}
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PROG
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(Python)
def c(n): return 1 if n==1 else s(n/2) if n%2==0 else s((n - 1)/2) + s((n + 1)/2)
def s(n): return 0 if n==1 else c(n/2) if n%2==0 else c((n - 1)/2) + c((n + 1)/2)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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