A154457 Signature-permutation of a Catalan bijection induced by wreath recursion a=s(b,c), b=s(c,a), c=(c,c), starting from state b.

0, 1, 3, 2, 8, 7, 6, 4, 5, 21, 22, 20, 18, 17, 19, 16, 14, 9, 10, 15, 11, 12, 13, 58, 59, 62, 63, 64, 57, 61, 55, 50, 49, 54, 48, 45, 46, 56, 60, 53, 47, 44, 51, 42, 37, 23, 24, 38, 25, 26, 27, 52, 43, 39, 28, 29, 40, 30, 31, 32, 41, 33, 34, 35, 36, 170, 171, 174, 175, 176

Offset

0,3

Comments

This Catalan bijection is induced by the second generator of group 2861 mentioned on page 144 of "Classification of groups generated by 3-state automata over a 2-letter alphabet" paper. Specifically, *A154457 = psi(A154447), 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 (*A154457! s) (cond ((pair? s) (*A069770! s) (*A154458! (car s)))) s)

Crossrefs

Inverse: A154458. a(n) = A057163(A154458(A057163(n))).

Sequence in context: A089859 A130958 A130397 * A073292 A073297 A127377

Adjacent sequences: A154454 A154455 A154456 * A154458 A154459 A154460

Keyword

nonn

Author

Antti Karttunen, Jan 17 2009

Status

approved