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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 (list; graph; refs; listen; history; text; internal format)
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 (non-root) nodes, so a(64)=2.

PROG

(Scheme:) (define (A106487 n) (cond ((zero? n) 1) (else (apply + (map A106487 (map shr (on-bit-indices n))))))) (define (shr n) (if (odd? n) (/ (- n 1) 2) (/ n 2))) (define (on-bit-indices 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

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.