0,3

Described in the fxtbook

List of binary words with parentheses for those in the sequence:

0 0000 P [empty string]

1 0001 P ()

2 0010

3 0011 P (())

4 0100

5 0101 P ()()

6 0110

7 0111 P ((()))

8 1000

9 1001

10 1010

11 1011 P (()())

12 1100

13 1101 P ()(())

14 1110

15 1111 P (((())))

C++ code that returns true if the input is a in the sequence: inline bool is_parenword(ulong x) { int s = 0; for (ulong j=0; x!=0; ++j) { s += ( x&1 ? +1 : -1 ); if ( s<0 ) break; // invalid word x >>= 1; } return (s>=0); }

Sequence in context: A141107 A047484 A036991 this_sequence A091892 A117203 A081118

Adjacent sequences: A100546 A100547 A100548 this_sequence A100550 A100551 A100552

nonn

Joerg Arndt (arndt(AT)jjj.de), Nov 27 2004