A384966 Number of sensed simple planar maps with n vertices and 2 faces.

0, 0, 1, 2, 8, 29, 113, 444, 1763, 6951, 27395, 107672, 422330, 1654180, 6472518, 25308760, 98923442, 386589398, 1510737079, 5904291401, 23079308104, 90236258057, 352908128341, 1380632536468, 5403055984114, 21152009997924, 82835786189975, 324518950873991, 1271797441923614, 4985982054721119

Offset: 1

Author

Andrew Howroyd, Jun 14 2025

Keywords

• nonn

Comments

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.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Column 2 of A384964.

Cf. A001429, A006078 (cycle is loop), A007595 (cycle is digon), A380237 (not necessarily simple), A384967 (unsensed version)..

Programs

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}

Formula

a(n) = A380237(n) - A007595(n) - A006078(n).