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A144964 Number of groves of degree n. 0
1, 3, 31, 16383, 4398046511103, 5444517870735015415413993718908291383295 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let Y_n be the set of trees of degree n. A nonempty subset of Y_n is called a grove. The set of all groves of degree n is denoted by Y_n. a(n) for n<= 7 given by rightmost column of Table 1, p. 3, of Bruno and Yasaki: The arithmetic of the natural numbers N can be extended to arithmetic operations on planar binary trees. This gives rise to a noncommutative arithmetic theory. In this exposition, we describe this arithmetree, first defined by Loday and investigate prime trees.

LINKS

Table of n, a(n) for n=1..6.

Adriano Bruno, Dan Yasaki, The arithmetic of trees, arXiv:0809.4448 [math.CO]

J.-L. Loday, Arithmetree, J. Algebra 258 (2002), no. 1, 275-309.

CROSSREFS

Cf. A000108.

Sequence in context: A002707 A283247 A261472 * A168678 A276199 A118913

Adjacent sequences:  A144961 A144962 A144963 * A144965 A144966 A144967

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Sep 27 2008

STATUS

approved

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Last modified August 19 15:50 EDT 2018. Contains 313878 sequences. (Running on oeis4.)