A007187 Leech's tree-labeling problem for n nodes. (Formerly M2532)

1, 3, 6, 9, 15, 20, 26, 34, 41

Offset

2,2

Comments

a(11) >= 48, a(12) >= 55.

a(n) is the greatest number k such that there exists a tree with n nodes and integral edge labels such that for each integer 1 <= m <= k, there exists a pair of nodes such that the sum of the edge labels on the path connecting the two nodes equals m. - Charlie Neder, Apr 26 2019

References

R. K. Guy, Unsolved Problems in Number Theory, Sect. C10.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=2..10.

R. K. Guy, A quarter century of "Monthly" unsolved problems, 1969-1993, Amer Math. Monthly, 100 (1993), 945-949.

J. Leech, On the representation of 1, 2, ..., n by differences, J. Lond. Math. Soc. 31 (1956), 160-169.

Index entries for sequences related to trees

Crossrefs

Cf. A005488.

Sequence in context: A368611 A143981 A031940 * A337502 A082004 A364017

Adjacent sequences: A007184 A007185 A007186 * A007188 A007189 A007190

Keyword

nonn,hard,nice,more

Author

N. J. A. Sloane

Status

approved