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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
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
Sequence in context: A153246 A358006 A025889 * A287356 A029402 A330443
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.)