A072768 The RASTxx transformation of the sequence A072643. The sizes of the parenthesizations produced by 'cons' combination A072764 & its transpose A072766.

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

1,2

Comments

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

Table of n, a(n) for n=1..105.

A. Karttunen, Gatomorphisms (Includes the complete Scheme source for computing this sequence)

N. J. A. Sloane, Transforms (Maple code for RASTxx transform)

Prog

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

Crossrefs

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

Sequence in context: A115777 A340033 A316847 * A071673 A174199 A072660

Adjacent sequences: A072765 A072766 A072767 * A072769 A072770 A072771

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 12 2002

Status

approved