Print the pattern using 0 and 1 only

---

I am working on a question which includes various tasks. There is requirement of printing such series:

0

01

001

0011

00010

000101

0001011

00010111

000010110

0000101100

00001011000

000010110000

0000101100101

00001011001011

000010110010110

0000101100101100

00001011001011000

000010110010110000

0000101100101100101

00001011001011001011

000010110010110010110

0000101100101100101100 .....

I tried almost everything and I'm unable to build the logic to do so.. Any hint I can get?