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 A384966 #10 Jun 15 2025 14:38:27
%S A384966 0,0,1,2,8,29,113,444,1763,6951,27395,107672,422330,1654180,6472518,
%T A384966 25308760,98923442,386589398,1510737079,5904291401,23079308104,
%U A384966 90236258057,352908128341,1380632536468,5403055984114,21152009997924,82835786189975,324518950873991,1271797441923614,4985982054721119
%N A384966 Number of sensed simple planar maps with n vertices and 2 faces.
%C A384966 In other words, a(n) is the number of embeddings on the sphere of connected simple unicyclic planar graphs with n nodes up to orientation preserving isomorphisms.
%H A384966 Andrew Howroyd, <a href="/A384966/b384966.txt">Table of n, a(n) for n = 1..1000</a>
%F A384966 a(n) = A380237(n) - A007595(n) - A006078(n).
%o A384966 (PARI) seq(n)={my(c(d)=(1-sqrt(1-4*x^d + O(x*x^(n+d))))/(2*x^d)); Vec(1/(1 - x*c(2)) - x*(c(1)^2 + c(2)) - x^2*(c(1)^4 + 3*c(2)^2)/2 - 1 - sum(k=1, n, log(2 - c(k))*eulerphi(k)/k), -n)/2}
%Y A384966 Column 2 of A384964.
%Y A384966 Cf. A001429, A006078 (cycle is loop), A007595 (cycle is digon), A380237 (not necessarily simple), A384967 (unsensed version)..
%K A384966 nonn
%O A384966 1,4
%A A384966 _Andrew Howroyd_, Jun 14 2025