A072768 The RASTxx transformation of the sequence A072643.

1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 4, 4, 5, 4, 4, 4, 5, 5, 5, 5, 4, 4, 5, 6, 5, 6, 5, 4, 4, 5, 6, 6, 6, 6, 5, 4, 4, 5, 6, 6, 7, 6, 6, 5, 4, 5, 5, 6, 6, 7, 7, 6, 6, 5, 5, 5, 6, 6, 6, 7, 7, 7, 6, 6, 6, 5, 5, 6, 7, 6, 7, 7, 7, 7, 6, 7, 6, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 5, 5, 6, 7, 7, 8, 7, 7, 7, 7, 8, 7, 7, 6, 5

Offset: 1

Author

Antti Karttunen, Jun 12 2002

Keywords

• nonn
• tabl

Comments

Also, the sizes of the parenthesizations produced by 'cons' combination A072764 and its transpose A072766.

Differs from A071673 first time at the position n=37, where A072768(37) = 4, while A071673(37) = 5. RASTxx(A072768) differs from A071673 first time at the position n=704, which leads to conjecture that the repeated applications of RASTxx starting from A072643 converge towards A071673, the fixed point of RASTxx transformation.

Each value v occurs A000108(v) times. (The term a(0)=0 is not explicitly listed here as to get a better looking triangle).

Links

• A. Karttunen, Gatomorphisms (Includes the complete Scheme source for computing this sequence)
• N. J. A. Sloane, Transforms (Maple code for RASTxx transform)

Crossrefs

Same triangle computed modulo 2: A072770. Permutations: A072643, A071673, A072644, A072645, A072660, A072789. Cf. also A072769, A025581, A002262.

Programs

Scheme

(define (A072768 n) (cond ((zero? n) n) (else (+ 1 (A072643 (A025581 (-1+ n))) (A072643 (A002262 (-1+ n)))))))