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 A381586 #19 Mar 07 2025 08:16:32
%S A381586 1,1,2,4,9,24,98,622,7293,162052,6997100,578605618,90558592724,
%T A381586 26673271109299,14758661765740616
%N A381586 Number of simple graphs on n unlabeled vertices whose degree sequence is consecutive.
%C A381586 A graph has a consecutive degree sequence if its distinct degrees are consecutive integers. This includes all regular graphs.
%D A381586 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).
%e A381586 For n = 4 there are 11 non-isomorphic graphs G on 4 vertices. An example with consecutive degree sequence is 4K_1, with degree sequence 0000; and an example with non-consecutive degree sequence is K_1 U K_3 with degree sequence 0222. The only other G with non-consecutive degree sequence is K_{1,3} with degree sequence 1113. Thus a(4) = 9.
%Y A381586 Cf. A000088, A005176.
%K A381586 nonn,more
%O A381586 0,3
%A A381586 _John P. McSorley_, Feb 28 2025
%E A381586 a(8)-a(14) from _Andrew Howroyd_, Feb 28 2025