A227193 Difference of (product of runlengths of 1-bits) and (product of runlengths of 0-bits) in binary representation of n.

0, 0, 0, 1, -1, 0, 1, 2, -2, -1, 0, 1, 0, 1, 2, 3, -3, -2, -1, 0, -1, 0, 1, 2, -1, 0, 1, 3, 1, 2, 3, 4, -4, -3, -2, -1, -3, -1, 0, 1, -2, -1, 0, 1, 0, 1, 2, 3, -2, -1, 0, 2, 0, 1, 3, 5, 0, 1, 2, 5, 2, 3, 4, 5, -5, -4, -3, -2, -5, -2, -1, 0, -5, -3, -1, 0, -2, 0

Offset: 0

Author

Antti Karttunen, Jul 08 2013

Keywords

• sign

Comments

The sequence seems to consist of palindromic subsequences centered around each (2^k)-1 and 2^k (with end points near the terms of A000975), which is easily explained by symmetric pairing of binary expansion of n and its complement.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10922

Crossrefs

Cf. A145037, A227190.

Programs

Maple

a:= proc(n) local i, j, m, r, s; m, r, s:= n, 1, 1;
      while m>0 do
        for i from 0 while irem(m, 2, 'h')=0 do m:=h od;
        for j from 0 while irem(m, 2, 'h')=1 do m:=h od;
        r, s:= r*j, s*max(i, 1)
      od; r-s
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 11 2013

Mathematica

a[n_] := With[{s = Split @ IntegerDigits[n, 2]}, Times @@ Length /@ Select[ s, First[#]==1&] - Times @@ Length /@ Select[s , First[#]==0&]]; Table[ a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 28 2016 *)

Scheme

(define (A227193 n) (- (A227349 n) (A227350 n)))

Formula

a(n) = A227349(n) - A227350(n).