A127284 a(n) = number of valleys (DU-steps) in the Dyck path encoded by A014486(n).

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

Links

Table of n, a(n) for n=0..101.

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

Adjacent sequences: A127281 A127282 A127283 * A127285 A127286 A127287

Keyword

nonn

Author

Antti Karttunen, Jan 16 2007

Status

approved