

A366142


MatulaGoebel numbers of rooted trees which are symmetrical about a straight line passing through the root.


0



1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 18, 19, 20, 23, 25, 27, 28, 31, 32, 36, 37, 44, 45, 48, 49, 50, 53, 59, 61, 63, 64, 67, 68, 71, 72, 75, 76, 80, 81, 83, 92, 97, 98, 99, 100, 103, 107, 108, 112, 121, 124, 125, 127, 128, 131, 144, 147, 148, 151, 153, 157, 162, 169, 171, 175, 176, 180
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OFFSET

1,2


COMMENTS

The MatulaGoebel number of a tree is Product prime(k_i), where the k_i are the MatulaGoebel numbers of the child subtrees of the root.
A tree is symmetric about a line iff the root has 2 copies of each child subtree (one each side of the line), and an optional "middle" child subtree on the line and in turn symmetric too.


LINKS



FORMULA

a(1) = 1; k > 1 is a term iff (k/p^2 is a term for some p) OR (k = prime(j) where j is a term).


EXAMPLE

12 is a term since it's the MatulaGoebel number of the following tree which is, per the layout shown, symmetric about the vertical.
(*)

(*) (*) (*)
\  /
\  /
(*) root


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



