A106487 Number of leaves in combinatorial game trees.

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

Offset: 0

Author

Antti Karttunen, May 21 2005

Keywords

• nonn

Comments

See the comment at A106486.

After n=0 differs from A000120 for the first time at n=64, where A000120(64)=1, while a(64)=2.

Examples

			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.
		

Crossrefs

Cf. A000120, A106486.

Programs

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)))))