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A227193 Difference of (product of runlengths of 1-bits) and (product of runlengths of 0-bits) in binary representation of n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
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
FORMULA
a(n) = A227349(n) - A227350(n).
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 *)
PROG
(Scheme) (define (A227193 n) (- (A227349 n) (A227350 n)))
CROSSREFS
Sequence in context: A179769 A340594 A361685 * A287397 A364204 A111407
KEYWORD
sign
AUTHOR
Antti Karttunen, Jul 08 2013
STATUS
approved

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Last modified March 4 22:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)