A127284 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	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: A117479 A118404 A089339 * A120691 A111941 A153462` `Adjacent sequences: A127281 A127282 A127283 * A127285 A127286 A127287`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 16 2007`

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Last modified February 17 14:19 EST 2012. Contains 206038 sequences.