This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A125989 #6 Jul 07 2025 16:13:43 %S A125989 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, %T A125989 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, %U A125989 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 %N A125989 Sum of heights of 10's in binary expansion of n. %C A125989 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. %e A125989 E.g. the lattice path /\/\ is encoded by 10 as 1010 in binary and both peaks occur at height=1, thus a(10)=2. %e A125989 In comparison, 11 is 1011 in binary, so the only peak '10' occurs at height -1: %e A125989 .../ %e A125989 /\/ %e A125989 thus a(11)=-1. %o A125989 (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)))))) %Y A125989 A126302 = a(A014486(n)). Cf. A085198. %K A125989 sign,base %O A125989 0,5 %A A125989 _Antti Karttunen_, Jan 02 2007