0,9

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 non-zero terms here). However, that is just a necessary but not a sufficient condition. For example, A123493 & A123494 satisfy it, but they still produce non-zero sequences: A153247, A153248.

(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)))))))

Cf. A082858, A153250, A153247, A153248.

Sequence in context: A030341 A121444 A118230 this_sequence A025889 A126306 A029402

Adjacent sequences: A153243 A153244 A153245 this_sequence A153247 A153248 A153249

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 22 2008