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A287731
Bisection of A287729.
3
1, 1, 2, 1, 1, 2, 3, 3, 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, 5, 7, 8, 7, 7, 8, 7, 5, 4, 5, 5, 4, 3, 3, 2, 1
OFFSET
1,3
COMMENTS
A287732(n)/a(n) enumerates all reduced fractions along the Stern-Brocot Tree. See the Serov link below.
FORMULA
a(n) = A287729(2*n-1), n > 0.
a(n) = A287730(n-1) + A287730(n), n > 0.
a(n) = A007306(n) - A287732(n) .
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;}
Then: c = a(n) and s = A287732(n);
PROG
(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)
def a(n): return c(2*n - 1) # Indranil Ghosh, Jun 08 2017
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
I. V. Serov, Jun 01 2017
STATUS
approved