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A057514
Number of peaks in mountain ranges encoded by A014486, number of leaves in the corresponding rooted plane trees (the root node is never counted as a leaf).
13
0, 1, 2, 1, 3, 2, 2, 2, 1, 4, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 1, 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, 2, 2, 2, 2, 1, 6, 5, 5, 5, 4, 5, 4, 5, 5, 4, 4, 4, 4, 3, 5, 4, 4, 4, 3, 5, 4, 5, 5, 4, 4, 4, 4, 3, 4, 3, 4, 4, 3, 4, 4, 4, 3, 3, 3, 3
OFFSET
0,3
COMMENTS
Sum_{i=A014137(n)..(A014137(n+1)-1)} a(i) = A001700(n), i.e., A001700(n) gives the total number of leaves in all ordered trees with n + 1 edges.
LINKS
Antti Karttunen, Gatomorphisms and other excursions ... (Includes Scheme program)
FORMULA
a(n) = A005811(A014486(n))/2 = A000120(A003188(A014486(n)))/2.
PROG
(Python)
def a005811(n): return bin(n^(n>>1))[2:].count("1")
def ok(n): # This function after Peter Luschny
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 0
return s==0
def A(n): return [0] + [i for i in range(1, n + 1) if ok(i)]
l=A(200)
print([a005811(l[i])//2 for i in range(len(l))]) # Indranil Ghosh, May 21 2017
CROSSREFS
a(n)-1 gives the number of zeros in A071153(n) (for n>=1).
Sequence in context: A084216 A347240 A308751 * A273568 A140720 A033559
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 03 2000
STATUS
approved