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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 23 13:30 EST 2020. Contains 332159 sequences. (Running on oeis4.)