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

Author

Antti Karttunen, Jan 17 2009

Keywords

• nonn

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

Crossrefs

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