Search: id:A106487
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%I A106487
%S A106487 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,
%T A106487 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,
%U A106487 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
%N A106487 Number of leaves in combinatorial game trees.
%C A106487 See the comment at A106486.
%e A106487 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.
%e A106487 64 = 2^6 = 2^(2*3), i.e. it encodes the CGT tree
%e A106487 \/
%e A106487 .\
%e A106487 which also has two terminal (non-root) nodes, so a(64)=2.
%o A106487 (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)))))
%Y A106487 Cf. After n=0 differs from A000120 for the first time at n=64, where 
               A000120(64)=1, while a(64)=2.
%Y A106487 Sequence in context: A105164 A000120 A105062 this_sequence A105102 A105105 
               A054717
%Y A106487 Adjacent sequences: A106484 A106485 A106486 this_sequence A106488 A106489 
               A106490
%K A106487 nonn
%O A106487 0,4
%A A106487 Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), May 21 2005

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