

A106487


Number of leaves in combinatorial game trees.


3



1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5
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OFFSET

0,4


COMMENTS

See the comment at A106486.


LINKS

Table of n, a(n) for n=0..101.


EXAMPLE

3 = 2^0 + 2^1 = 2^(2*0) + 2^((2*0)+1) encodes the CGT tree \/ which has two terminal nodes, thus a(3)=2.
64 = 2^6 = 2^(2*3), i.e. it encodes the CGT tree
\/
.\
which also has two terminal (nonroot) nodes, so a(64)=2.


PROG

(Scheme:) (define (A106487 n) (cond ((zero? n) 1) (else (apply + (map A106487 (map shr (onbitindices n))))))) (define (shr n) (if (odd? n) (/ ( n 1) 2) (/ n 2))) (define (onbitindices n) (let loop ((n n) (i 0) (c (list))) (cond ((zero? n) (reverse! c)) ((odd? n) (loop (/ ( n 1) 2) (1+ i) (cons i c))) (else (loop (/ n 2) (1+ i) c)))))


CROSSREFS

Cf. After n=0 differs from A000120 for the first time at n=64, where A000120(64)=1, while a(64)=2.
Sequence in context: A105164 A000120 A105062 * A105102 A105105 A178677
Adjacent sequences: A106484 A106485 A106486 * A106488 A106489 A106490


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 21 2005


STATUS

approved



