1,1

Replacing "1" by "(" and "0" by ")" yields well-formed bracket expressions (), ()(), (()), ()()(), ()(()), (())(), (()()), ((())), ()()()(), ()()(()), ()(())(), ()(()()), ()((())), (())()(), (())(()), (()())(), (()()()), (()(())), ((()))(), ((())()), ((()())), (((()))), ()()()()(), ()()()(()), ()()(())(), ()()(()()), ()()((())), ()(())()(), ()(())(()), ()(()())(), ()(()()()), ()(()(())), ()((()))(), ()((())()), ()((()())), ()(((()))), (())()()(), (())()(()), (())(())(), (())(()()), (())((())), (()())()(), (()())(()), (()()())(), (()()()()), (()()(())), (()(()))(), (()(())()), (()(()())), (()((()))), ((()))()(), ((()))(()), ((())())(), ((())()()), ((())(())), ((()()))(), ((()())()), ((()()())), ((()(()))), (((())))(), (((()))()), (((())())), (((()()))), ((((()))))

A. Karttunen, Illustration of initial terms up to size n=7

A. Karttunen, Gatomorphisms and other excursions ... (Includes Scheme program)

Chomsky-2 grammar with axiom s, terminal alphabet {0, 1}, and three rules s -> ss, s -> 1s0, s ->10

s -> ss -> 1s0s -> 11s00s -> 111000s -> 11100010

a(n) = A071152(n)/2. A014486 gives these terms as converted from decimal to binary system. Cf. also A071153.

Sequence in context: A104486 A098753 A066489 this_sequence A075166 A071671 A075171

Adjacent sequences: A063168 A063169 A063170 this_sequence A063172 A063173 A063174

base,nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jul 09 2001