

A071673


Sequence a(n) obtained by setting a(0) = 0; then reading the table T(x,y)=a(x)+a(y)+1 in antidiagonal fashion.


12



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, 5, 5, 6, 6, 7, 6, 6, 5, 5, 5, 6, 6, 6, 7, 7, 6, 6, 6, 5, 4, 6, 7, 6, 7, 7, 7, 6, 7, 6, 4, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 6, 6, 7, 8, 7, 7, 7, 8, 7, 6, 6, 5, 6, 6, 7, 6, 8, 8, 7, 7, 8, 8, 6, 7, 6, 6
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OFFSET

1,2


COMMENTS

The fixed point of RASTxx transformation. The repeated applications of RASTxx starting from A072643 seem to converge toward this sequence. Cf. A072768 from which this differs first time at the position n=37, where A072768(37) = 4, while A071673(37) = 5.
Each value v occurs A000108(v) times. (The term a(0)=0 is not explicitly listed here as to get a better looking triangle).
The size of each Catalan structure encoded by the corresponding terms in triangles A071671 & A071672 (i.e. the number of digits / 2), as obtained with the global ranking/unranking scheme presented in A071651A071654.


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)


FORMULA

a(0)=0, a(n)=1+a(A025581(n1))+a(A002262(n1))


EXAMPLE

E.g. we have a(1) = T(0,0) = a(0)+a(0)+1 = 1, a(2)=T(1,0)=a(1)+a(0)+1 = 2, a(3)=T(0,1)=a(0)+a(1)+1 = 2, a(4)=T(2,0)=a(2)+a(0)+1 = 3, etc.


PROG

(Scheme function:) (define (A071673 n) (cond ((zero? n) n) (else (+ 1 (A071673 (A025581 (1+ n))) (A071673 (A002262 (1+ n)))))))


CROSSREFS

Same triangle computed modulo 2: A071674. Permutations: A072643, A072644, A072645, A072660, A072768, 072789. Max. position where value v occurs: A072638(v). Cf. also A025581, A002262.
Sequence in context: A115777 A316847 A072768 * A174199 A072660 A237720
Adjacent sequences: A071670 A071671 A071672 * A071674 A071675 A071676


KEYWORD

nonn,tabl,eigen


AUTHOR

Antti Karttunen, May 30 2002. Selfreferential definition added Jun 03 2002.


STATUS

approved



