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A366142
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Matula-Goebel numbers of rooted trees which are symmetrical about a straight line passing through the root.
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0
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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
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1,2
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COMMENTS
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The Matula-Goebel number of a tree is Product prime(k_i), where the k_i are the Matula-Goebel 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.
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LINKS
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FORMULA
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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).
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EXAMPLE
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12 is a term since it's the Matula-Goebel number of the following tree which is, per the layout shown, symmetric about the vertical.
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(*) (*) (*)
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(*) root
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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