A382021 Number of distinct degree sequences among all simple graphs with n vertices whose degrees are consecutive integers.

1, 1, 2, 4, 9, 21, 50, 118, 272, 614, 1368, 3014

Offset: 0

Author

John P. McSorley, Mar 12 2025

Keywords

• nonn
• more

Comments

A sequence of integers is consecutive if its distinct entries are consecutive integers, and a graphic sequence is a sequence of integers that can be the degree sequence of some graph. Thus a(n) is the number of consecutive graphic sequences of length n.

Examples

			For n = 5 there are 34 non-isomorphic graphs G on 5 vertices, and 24 of these have a consecutive degree sequence. However consecutive degree sequences 11222, 12223, and 22233 each correspond to 2 non-isomorphic graphs. Thus there are 21 distinct consecutive graphic sequences of length 5, and so a(5)=21.
		

References

• R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).

Crossrefs

Cf. A381586, A000088, A004251, A005176.

Extensions

a(11) from Sean A. Irvine, Mar 18 2025