A153246 Number of fleeing trees computed for Catalan bijection A057164.

0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3

Offset

0,9

Comments

A "fleeing tree" sequence computed for Catalan bijection CatBij gives for each binary tree A014486(n) the number of cases where, when a new V-node (a bud) is inserted into one of the A072643(n)+1 possible leaves of that tree, it follows that (CatBij tree) is not a subtree of (CatBij tree-with-bud-inserted). I.e., for each tree A014486(n), we compute Sum_{i=0}^A072643(n) (1 if catbij(n) is a subtree of catbij(A153250bi(n,i)), 0 otherwise). Here A153250 gives the bud-inserting operation. Note that for any Catalan Bijection, which is an image of "psi" isomorphism (see A153141) from the Automorphism Group of infinite binary trees, the result will be A000004, the zero-sequence. To satisfy that condition, CatBij should at least satisfy A127302(CatBij(n)) = A127302(n) for all n (clearly A057164 does not satisfy that, so we got nonzero terms here). However, that is just a necessary but not a sufficient condition. For example, A123493 & A123494 satisfy it, but they still produce nonzero sequences: A153247, A153248.

Links

Table of n, a(n) for n=0..101.

Prog

(MIT Scheme:)
(define (A153246 n) (count-fleeing-trees n A057164))
(define (count-fleeing-trees n catbij) (add (lambda (i) (if (= (A082858bi (catbij (A153250bi n i)) (catbij n)) (catbij n)) 0 1)) 0 (A072643 n)))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

Crossrefs

Cf. A082858, A153250, A153247, A153248.

Sequence in context: A121444 A118230 A179181 * A358006 A025889 A126306

Adjacent sequences: A153243 A153244 A153245 * A153247 A153248 A153249

Keyword

nonn

Author

Antti Karttunen, Dec 22 2008

Status

approved