0,3

CatalanRankGlobal given in A057117 and the other Maple procedures in A056539.

Composition with A057163 gives Donaghey's Map M (A057505/A057506).

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

A. Karttunen, C-program which implements this gatomorphism

Index entries for signature-permutations induced by Catalan automorphisms

a(n) = A080300(A036044(A014486(n))) = A080300(A056539(A014486(n))).

a(10)=14 and a(14)=10, A014486[10] = 172 (10101100 in binary), A014486[14] = 202 (11001010 in binary) and these encode the following mountain ranges (and the corresponding rooted plane trees), which are reflections of each other:

...../\___________/\

/\/\/__\_________/__\/\/\

...

...../...........\

..\|/.............\|/

a(n) = CatalanRankGlobal(runcounts2binexp(reverse(binexp2runcounts(A014486[n])))) [i.e. reverse and complement the totally balanced binary sequences]

(Scheme function implementing this automorphism on list-structures:) (define (DeepRev lista) (cond ((not (pair? lista)) lista) ((null? (cdr lista)) (cons (DeepRev (car lista)) (list))) (else (append (DeepRev (cdr lista)) (DeepRev (cons (car lista) (list)))))))

A057123[A057163[n]] = A057164[A057123[n]] for all n. Also the car/cdr-flipped conjugate of A069787, i.e. A057164(n) = A057163(A069787(A057163(n))). Fixed terms are given by A061856. Cf. also A057508, A069772.

Row 2 of tables A122287 and A122288.

Sequence in context: A073285 A057512 A057508 this_sequence A085175 A130111 A104182

Adjacent sequences: A057161 A057162 A057163 this_sequence A057165 A057166 A057167

nonn

Antti Karttunen Aug 18 2000