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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.
3
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).
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 17 2009
STATUS
approved