A380238 Number of achiral planar maps with n vertices and 2 faces.

1, 2, 5, 12, 28, 68, 157, 372, 845, 1949, 4367, 9880, 21858, 48679, 106612, 234546, 509246, 1109352, 2391299, 5167423, 11070598, 23762557, 50641725, 108085708, 229303142, 487039228, 1029167119, 2176808877, 4583856878, 9660020146, 20279242545, 42599286814

Offset

1,2

Comments

Also by duality the number of achiral 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

Prog

(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}
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(1 - x^k*c(m*k)^(2/m))*eulerphi(k)/k, O(x*x^n))}
seq(n)={Vec(G1(n)+G2(n))/2}

Crossrefs

Column 2 of A379431.

Cf. A380237 (sensed), A380239 (unsensed).

Sequence in context: A166297 A024960 A291234 * A346051 A362893 A326760

Adjacent sequences: A380235 A380236 A380237 * A380239 A380240 A380241

Keyword

nonn

Author

Andrew Howroyd, Jan 19 2025

Status

approved