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A235112
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a(n) = the largest of the M-indices of the trees with n vertices.
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1
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1, 2, 3, 7, 16, 32, 64, 152, 361, 1273, 4489, 22177, 109561, 735151
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OFFSET
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1,2
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COMMENTS
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We define the M-index of a tree T to be the smallest of the Matula numbers of the rooted trees isomorphic (as a tree) to T. Example. The path tree P[5] = ABCDE has M-index 9. Indeed, there are 3 rooted trees isomorphic to P[5]: rooted at A, B, and C, respectively. Their Matula numbers are 11, 10, and 9, respectively. Consequently, the M-index of P[5] is 9.
a(n) = largest (= last) entry in row n of A235111.
It is conjectured that for n>=7 one has a(n) = A235120(n-6).
These numbers can be useful, for example, in the following situation. We intend to identify all trees that have 10 vertices and satisfy a certain property. Instead of scanning all rooted trees with Matula numbers from A005517(10)=125 to A005518(10)=219613, we do the scanning only for Matula numbers between 125 and a(10)=1273.
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LINKS
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FORMULA
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EXAMPLE
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a(4)=7. Indeed, there are 2 trees with 4 vertices: the path P[4] and the star S[3] with 3 edges. There are two rooted trees isomorphic to P[4]; they have Matula numbers 5 and 6; so the M-index is 5. There are two rooted trees isomorphic to S[3]; they have Matula numbers 7 and 8; so the M-index is 7. Max(5,7) = 7.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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