A126306 - OEIS

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A126306

a(n) = number of double-rises (UU-subsequences) in the n-th Dyck path encoded by A014486(n).

0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 3, 0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 1, 2, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 3 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,9`
	FORMULA	`a(n) = A014081(A014486(n)).`
	EXAMPLE	`A014486(20) = 228 (11100100 in binary), encodes the following Dyck path:` `../\` `./..\/\` `/......\` `and there is one rising (left-hand side) slope with length 3 and one with length 1, so in the first slope, consisting of 3 U-steps, there are two cases with two consecutive U-steps (overlapping is allowed), thus a(20)=2.`
	CROSSREFS	`a(n) = A000120(A048735(A014486(n))). a(A125976(n)) = A057514(n)-1, for all n >= 1.` `Sequence in context: A179181 A153246 A025889 * A029402 A035196 A158020` `Adjacent sequences: A126303 A126304 A126305 * A126307 A126308 A126309`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 02 2007`

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Last modified February 17 02:31 EST 2012. Contains 205978 sequences.