|
| |
| |
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,4
|
|
|
COMMENTS
|
a(n)/A287731(n) enumerates all reduced fractions along the Stern-Brocot Tree. See the Serov link below.
|
|
|
LINKS
|
I. V. Serov, Table of n, a(n) for n = 1..8192
I. V. Serov, OEIS: The Stern-Brocot Tree as Sequence A287732/A287731
N. J. A. Sloane, Stern-Brocot or Farey Tree
Index entries for fraction trees
Index entries for sequences related to Stern's sequences
|
|
|
FORMULA
|
a(n) = A287730(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 = A287731(n) and s = a(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 s(2*n - 1) # Indranil Ghosh, Jun 08 2017
|
|
|
CROSSREFS
|
Cf. A002487, A007306, A287729, A287730, A287731.
Sequence in context: A123548 A131838 A274885 * A334223 A171414 A270921
Adjacent sequences: A287729 A287730 A287731 * A287733 A287734 A287735
|
|
|
KEYWORD
|
nonn,frac
|
|
|
AUTHOR
|
I. V. Serov, Jun 01 2017
|
|
|
STATUS
|
approved
|
| |
|
|
