A154458 Signature-permutation of a Catalan bijection induced by wreath recursion a=s(b,c), b=s(c,a), c=(c,c), starting from state a.

0, 1, 3, 2, 7, 8, 6, 5, 4, 17, 18, 20, 21, 22, 16, 19, 15, 13, 12, 14, 11, 9, 10, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 44, 47, 53, 56, 60, 43, 52, 41, 35, 36, 40, 34, 32, 31, 42, 51, 39, 33, 30, 37, 28, 23, 24, 38, 29, 25, 26, 27, 129, 130, 132, 133, 134

Offset

0,3

Comments

This Catalan bijection is induced by the first generator of group 2861 mentioned on page 144 of "Classification of groups generated by 3-state automata over a 2-letter alphabet" paper. Specifically, *A154458 = psi(A154448), where the isomorphism psi is given in A153141 (see further comments there).

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

Bondarenko, Grigorchuk, Kravchenko, Muntyan, Nekrashevych, Savchuk, Sunic, Classification of groups generated by 3-state automata over a 2-letter alphabet, p. 144.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154458! s) (cond ((pair? s) (*A069770! s) (*A154457! (cdr s)))) s)

Crossrefs

Inverse: A154457. a(n) = A057163(A154457(A057163(n))).

Sequence in context: A323710 A089863 A069767 * A127378 A122302 A131159

Adjacent sequences: A154455 A154456 A154457 * A154459 A154460 A154461

Keyword

nonn

Author

Antti Karttunen, Jan 17 2009

Status

approved