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A358650
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Matula-Goebel tree number of the binomial tree of n vertices.
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1
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1, 2, 4, 6, 12, 18, 42, 78, 156, 234, 546, 1014, 2886, 4758, 14118, 30966, 61932, 92898, 216762, 402558, 1145742, 1888926, 5604846, 12293502, 28210026, 45860646, 121727346, 249864654, 813198126, 1423166394, 4740553974, 11234495766, 22468991532, 33703487298
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OFFSET
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1,2
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COMMENTS
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The top-down definition of the binomial tree suits Matula-Goebel numbering: The tree of n = 2^k + r vertices, for 1 <= r <= 2^k is the binomial tree of 2^k vertices and a child subtree under the root which is the binomial tree of r vertices.
In the tree of n vertices, adding a new singleton child under each vertex gives the tree of 2*n vertices, so that a(2*n) = A348067(a(n)).
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LINKS
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FORMULA
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a(2^k + r) = a(2^k) * prime(a(r)) for 1 <= r <= 2^k.
a(2^k) = A076146(k+1), being a tree of order k.
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EXAMPLE
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The tree of n=13 vertices numbered 0..12 is
0
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1 2 4 8
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3 5 6 9 10 12
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7 11
Vertices 0..7 are the binomial tree of 2^k = 8 vertices, and vertices 8..12 are the binomial tree of 5 vertices.
Using the recurrence, a(13) = a(8 + 5) = a(8) * prime(a(5)) = 78*37 = 2886.
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PROG
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(PARI) See links.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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