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

Author

Antti Karttunen, Jan 16 2007

Keywords

• nonn

Examples

			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.
		

Crossrefs

a(A057163(n)) = A126306(n), a(n) = A126306(A057163(n)) for all n. Cf. A057516.

Programs

Scheme

(define (A127284 n) (if (zero? n) 0 (- (A057514 n) 1)))

Formula

a(0)=0, a(n) = A057514(n)-1.