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 A381765 #41 Apr 02 2025 03:56:04
%S A381765 1,1,1,2,5,16,75,544,6920,159228,6961507,577826609,90529308665
%N A381765 Number of connected simple graphs on n unlabeled vertices whose degree sequence is consecutive.
%C A381765 A connected graph has a consecutive degree sequence if its distinct degrees are consecutive integers. This includes all connected regular graphs.
%D A381765 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).
%e A381765 For n = 4 there are 6 non-isomorphic connected graphs G on 4 vertices. An example with consecutive degree sequence is P_4, the path on 4 vertices, with degree sequence 1122; and an example with non-consecutive degree sequence is the star K_{1,3} with degree sequence 1113. All other connected G have consecutive degree sequence. Thus a(4) = 5.
%Y A381765 Cf. A381586, A001349, A005177.
%K A381765 nonn,more
%O A381765 0,4
%A A381765 _John P. McSorley_, Mar 25 2025
%E A381765 a(7)-a(10) from _Andrew Howroyd_, Mar 26 2025
%E A381765 a(11)-a(12) from _Sean A. Irvine_, Apr 01 2025