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A106487
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Number of leaves in combinatorial game trees.
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3
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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; internal format)
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OFFSET
| 0,4
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COMMENTS
| See the comment at A106486.
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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.
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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)))))
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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
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), May 21 2005
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