A125989 Sum of heights of 10's in binary expansion of n.

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

Offset: 0

Author

Antti Karttunen, Jan 02 2007

Keywords

• sign
• base

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.

Examples

			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.
		

Crossrefs

A126302 = a(A014486(n)). Cf. A085198.

Programs

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))))))