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 A126306 a(n) = number of double-rises (UU-subsequences) in the n-th Dyck path encoded by A014486(n). 3
 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; text; internal format)
 OFFSET 0,9 LINKS Table of n, a(n) for n=0..101. FORMULA a(n) = A014081(A014486(n)). a(n) = A000120(A048735(A014486(n))). a(A125976(n)) = A057514(n)-1, for all n >= 1. 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. PROG (Python) def ok(n): if n==0: return True B=bin(n)[2:] if n!=0 else '0' s=0 for b in B: s+=1 if b=='1' else -1 if s<0: return False return s==0 def a014081(n): return sum(((n>>i)&3==3) for i in range(len(bin(n)[2:]) - 1)) print([a014081(n) for n in range(4001) if ok(n)]) # Indranil Ghosh, Jun 13 2017 CROSSREFS Cf. A014081, A014486, A000120, A048735, A125976, A057514. Sequence in context: A153246 A358006 A025889 * A287356 A029402 A330443 Adjacent sequences: A126303 A126304 A126305 * A126307 A126308 A126309 KEYWORD nonn AUTHOR Antti Karttunen, Jan 02 2007 STATUS approved

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Last modified February 29 23:21 EST 2024. Contains 370428 sequences. (Running on oeis4.)