A379102 Number of fundamentally distinct graceful labelings in a maximally graceful tree with n vertices.

1, 1, 1, 1, 3, 6, 18, 52, 114, 367, 1777, 5249, 21107, 84746, 432769, 10399350

Offset

1,5

Comments

Values appearing in Fig. 6 of Anick (2016) count subtractively complemented labelings separately and so must be divided by 2 to obtain what are conventionally considered "fundamentally distinct" labelings (i.e., distinct both with respect to the symmetry of the graph *and* subtractive complementation with respect the edge count of a graph).

References

D. E. Knuth, The Art of Computer Programing, Vol. 4, Section 7.2.2.3. In preparation.

Links

Table of n, a(n) for n=1..16.

David Anick, Counting graceful labelings of trees: a theoretical and empirical study, Discrete Applied Mathematics 198 (2016), 65-81.

Eric Weisstein's World of Mathematics, Maximally Graceful Tree.

Crossrefs

Sequence in context: A148563 A148564 A148565 * A112572 A089325 A110593

Adjacent sequences: A379099 A379100 A379101 * A379103 A379104 A379105

Keyword

nonn,more

Author

Eric W. Weisstein, Dec 28 2024

Status

approved