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 A291648 #25 Sep 12 2017 11:02:26 %S A291648 1,2,4,9,19,45,105,261,657,1708,4498,12081,32752,89792,247893,689004, %T A291648 1924357,5398587,15197830,42917215,121507597,344806293,980423528, %U A291648 2792741331,7967842859,22765631866,65131178683,186560990191,53497417058,1535637252938 %N A291648 a(n) is the number of simple graphs of order n having at most one cycle (such graphs are called "at most unicyclic graphs"). %C A291648 a(n) = A005195(n) + A236570(n). Proof: Since an at most unicyclic graph is either a forest or a unicyclic graph and since the latter two types of graphs have been enumerated (see A005195, A236570) the enumeration of the at most unicyclic graphs is the sum of the enumeration of the forests and unicyclic graphs, namely, the sum of the sequences A005195 and A236570, where these sequences start for n >= 1, respectively, %C A291648 1, 2, 3, 6, 10, 20, 37, 76, ... %C A291648 0, 0, 1, 3, 9, 25, 68 185, ... . %H A291648 E. G. DuCasse, L. V. Quintas, and J. M. Zorluoglu, <a href="/A291648/a291648.pdf">The At Most Unicyclic Random Graph Process</a>, Mathematics Department, Pace University, New York, No. 1 (2017). %e A291648 For n = 4, a(4) = 6 + 3 = 9 and for n = 5, a(5) = 10 + 9 = 19 %Y A291648 Cf. A005195 (number of forests with n unlabeled nodes), A236570 (number of n-node unicyclic graphs). %K A291648 nonn %O A291648 1,2 %A A291648 _Louis V QUINTAS_, Aug 28 2017