0,1

Meeussen's observation about the orbits of a composition of two involutions F and R states that if the orbit size of the composition (acting on a particular element of the set) is odd, then it contains an element fixed by the other involution if and only if it contains also an element fixed by the other, on the (almost) opposite side of the cycle. Here those two involutions are A057163 and A057164, their composition is Donaghey's "Map M" A057505, and as the trees A080293/A080295 are symmetric as binary trees, and the cycle sizes A080292 are odd, it follows that these are symmetric as general trees.

A. Karttunen, Initial terms illustrated

a(n) = A014486(A080975(n)) = A014486(A057505^((A080292(n)+1)/2) (A080293(n))) [where ^ stands for the repeated applications of permutation A057505.]

Same sequence in binary: A080974. A036044(a(n)) = a(n) for all n. The number of edges (as general trees): A080978.

Sequence in context: A099882 A121293 A057106 this_sequence A079179 A000654 A061306

Adjacent sequences: A080970 A080971 A080972 this_sequence A080974 A080975 A080976

nonn

Antti Karttunen (my_firstname.my_surname(AT)iki.fi) Mar 02 2003