

A125989


Sum of heights of 10's in binary expansion of n.


2



0, 0, 1, 0, 2, 0, 1, 0, 3, 1, 2, 1, 2, 0, 1, 0, 4, 2, 3, 0, 4, 0, 1, 2, 3, 1, 2, 1, 2, 0, 1, 0, 5, 3, 4, 1, 5, 1, 2, 1, 6, 2, 3, 2, 3, 1, 0, 3, 4, 2, 3, 0, 4, 0, 1, 2, 3, 1, 2, 1, 2, 0, 1, 0, 6, 4, 5, 2, 6, 2, 3, 0, 7, 3, 4, 1, 4, 0, 1, 2, 8, 4, 5, 0, 6, 0, 1, 4, 5, 1, 2, 3, 2, 2, 1
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OFFSET

0,5


COMMENTS

The 'height' of the digits in the binary expansion of n is here defined by the algorithm where, starting from the least significant bit and the height=0 and proceeding leftwards, all encountered 1bits decrease the height by one and all 0bits increase it by one. The sequence gives the sums of heights at the positions where 0 changes to 1 when scanning the binary expansion from right to left. This sequence is used for computing A126302.


LINKS

Table of n, a(n) for n=0..94.


EXAMPLE

E.g. the lattice path /\/\ is encoded by 10 as 1010 in binary and both peaks occur at height=1, thus a(10)=2.
In comparison, 11 is 1011 in binary, so the only peak '10' occurs at height 1:
.../
/\/
thus a(11)=1.


PROG

(Scheme:) (define (A125989 n) (let loop ((n n) (s 0) (h 0)) (cond ((zero? n) s) ((= 2 (modulo n 4)) (loop (/ ( n 2) 4) (+ s h 1) h)) ((odd? n) (loop (/ ( n 1) 2) s ( h 1))) (else (loop (/ n 2) s (+ 1 h))))))


CROSSREFS

A126302 = a(A014486(n)). Cf. A085198.
Sequence in context: A245151 A243978 A106844 * A125924 A283929 A082513
Adjacent sequences: A125986 A125987 A125988 * A125990 A125991 A125992


KEYWORD

sign,base


AUTHOR

Antti Karttunen, Jan 02 2007


STATUS

approved



