A380239 Number of unsensed planar maps with n vertices and 2 faces.

1, 2, 5, 13, 35, 104, 315, 1021, 3407, 11814, 41893, 151688, 556432, 2063446, 7709381, 28977788, 109421539, 414759097, 1577080457, 6013019088, 22980514005, 88012484058, 337717418145, 1298113689274, 4997561829650, 19267942661664, 74386901833067, 287540841925770

Offset: 1

Author

Andrew Howroyd, Jan 19 2025

Keywords

• nonn

Comments

Also by duality the number of unsensed planar maps with n faces and 2 vertices.

The number of edges is n.

Links

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

Crossrefs

Column 2 of A277741.

Cf. A380237 (sensed), A380238 (achiral).

Programs

PARI

G1(n)={my(g=(1-sqrt(1-4*x^2 + O(x*x^n)))/(2*x^2)); ((1 + x/(1-x-x^2*g)^2)^2/(1 - x^2*g^2) - 1)/2 + 1/(1 - x*g) - 1}
G2(n)={my(c(d)=(1-sqrt(1-4*x^d + O(x*x^(n+d))))/(2*x^d)); sum(k=1, n, my(m=1+k%2); -(log(2 - c(k)) + log(1 - x^k*c(m*k)^(2/m)))*eulerphi(k)/k, O(x*x^n))}
seq(n)={Vec(G1(n)+G2(n))/4}

Formula

a(n) = (A380237(n) + A380238(n))/2.