This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382021 #9 Mar 18 2025 21:14:02 %S A382021 1,1,2,4,9,21,50,118,272,614,1368,3014 %N A382021 Number of distinct degree sequences among all simple graphs with n vertices whose degrees are consecutive integers. %C A382021 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. %D A382021 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999). %e A382021 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. %Y A382021 Cf. A381586, A000088, A004251, A005176. %K A382021 nonn,more %O A382021 0,3 %A A382021 _John P. McSorley_, Mar 12 2025 %E A382021 a(11) from _Sean A. Irvine_, Mar 18 2025