login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I #28 Mar 25 2021 10:21:10

%S 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,

%T 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,

%U 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

%N 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).

%C 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.

%H Indranil Ghosh, <a href="/A057514/b057514.txt">Table of n, a(n) for n = 0..3485</a>

%H Antti Karttunen, <a href="http://web.archive.org/web/20050429191204/http://ndirty.cute.fi/%7Ekarttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms and other excursions ...</a> (Includes Scheme program)

%H Antti Karttunen, <a href="https://github.com/karttu/IntSeq/tree/master/src/Uncleaned/Catalania">Newer version of the Scheme code collection</a>

%F a(n) = A005811(A014486(n))/2 = A000120(A003188(A014486(n)))/2.

%o (Python)

%o def a005811(n): return bin(n^(n>>1))[2:].count("1")

%o def ok(n): # This function after _Peter Luschny_

%o B=bin(n)[2:] if n!=0 else 0

%o s=0

%o for b in B:

%o s+=1 if b=="1" else -1

%o if s<0: return 0

%o return s==0

%o def A(n): return [0] + [i for i in range(1, n + 1) if ok(i)]

%o l=A(200)

%o print([a005811(l[i])//2 for i in range(len(l))]) # _Indranil Ghosh_, May 21 2017

%Y Cf. A000108, A000120, A001700, A003188, A005811, A014137, A014486, A057515.

%Y a(n)-1 gives the number of zeros in A071153(n) (for n>=1).

%K nonn

%O 0,3

%A _Antti Karttunen_, Sep 03 2000

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)