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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 (list; graph; refs; listen; history; text; internal format)
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 1-bits decrease the height by one and all 0-bits 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

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Last modified February 24 11:12 EST 2018. Contains 299603 sequences. (Running on oeis4.)