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 A382665 #9 Apr 09 2025 22:54:37 %S A382665 1,1,1,2,5,14,35,88,212,492,1122 %N A382665 Number of distinct degree sequences among all connected simple graphs with n vertices whose degrees are consecutive integers. %C A382665 A sequence of integers is consecutive if its distinct entries are consecutive integers, and a graphic sequence is a sequence of integers that is the degree sequence of some graph. Thus a(n) is the number of graphic sequences of length n that are consecutive and represent a connected graph. %D A382665 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999). %e A382665 For n = 5 there are 21 non-isomorphic connected graphs G on 5 vertices, and 16 of these have a consecutive degree sequence. However consecutive degree sequences 12223, and 22233 each correspond to 2 non-isomorphic connected graphs. Thus there are 14 distinct graphic sequences of length 5 that are consecutive and represent a connected graph, and so a(5)=14. %Y A382665 Cf. A001349, A381765, A382021. %K A382665 nonn,more %O A382665 0,4 %A A382665 _John P. McSorley_, Apr 02 2025 %E A382665 a(7)-a(10) from _Andrew Howroyd_, Apr 02 2025