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A127284
a(n) = number of valleys (DU-steps) in the Dyck path encoded by A014486(n).
2
0, 0, 1, 0, 2, 1, 1, 1, 0, 3, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 0, 4, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 1, 3, 2, 3, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 0, 5, 4, 4, 4, 3, 4, 3, 4, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 2, 4, 3, 4, 4, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 2
OFFSET
0,5
FORMULA
a(0)=0, a(n) = A057514(n)-1.
EXAMPLE
A014486(2) = 10 (1010 in binary) which encodes Dyck path /\/\ with two peaks and one valley, thus a(2)=1.
A014486(12) = 180 (10110100 in binary) which encodes Dyck path:
..../\/\...
./\/....\..
which has two valleys, thus a(12) = 2.
PROG
(Scheme:) (define (A127284 n) (if (zero? n) 0 (- (A057514 n) 1)))
CROSSREFS
a(A057163(n)) = A126306(n), a(n) = A126306(A057163(n)) for all n. Cf. A057516.
Sequence in context: A182662 A308778 A372472 * A120691 A111941 A153462
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 16 2007
STATUS
approved

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Last modified September 20 17:04 EDT 2024. Contains 376075 sequences. (Running on oeis4.)