A126312 Fixed points of permutation A071661/A071662.

0, 1, 2, 3, 4, 8, 9, 22, 23, 30, 55, 64, 65, 98, 158, 196, 197, 318, 484, 625, 626, 687, 1042, 1549, 1973, 2055, 2056, 2376, 3471, 5113, 6558, 6917, 6918, 8191, 11763, 17268, 22277, 23713, 23714, 24331, 28360, 40491, 59362, 76942, 81754, 82499

Offset

0,3

Comments

Those i for which A071661(i)=i, i.e. for which A057163(A057164(i)) = A057164(A057163(i)). These appear to consist of just those general plane trees which are symmetric and will stay symmetric also after the underlying plane binary tree has been reflected, i.e. for which A057164(i)=i and A057164(A057163(i)) = A057163(i). See comments at A123050 and A080070. The sequence seems to give also the fixed points of the permutation A125977/A125978.

Links

Table of n, a(n) for n=0..45.

D. Callan, A Bijection on Dyck Paths and Its Cycle Structure, 2006, 17pp.

Crossrefs

Sequence in context: A078830 A304521 A026489 * A126298 A175404 A292113

Adjacent sequences: A126309 A126310 A126311 * A126313 A126314 A126315

Keyword

nonn

Author

Antti Karttunen, Jan 16 2007

Status

approved