A377785 Number of n-node connected unsensed planar maps with an external face in which all internal faces are triangles.

1, 2, 5, 19, 80, 407, 2403, 15570, 107366, 773660, 5746826, 43693041, 338367370, 2660629311, 21193182914, 170714892489, 1388711749891, 11395477091396, 94238431709661, 784796579069288, 6576997589788217, 55435506835745851, 469698698872829672, 3998806331800289798

Offset: 3

Author

Ya-Ping Lu, Nov 06 2024

Keywords

• nonn

Comments

Maps for a(3) through a(7) are illustrated in Links.

The planar maps considered are without loops or isthmuses.

In other words, a(n) is the number of embeddings in the plane of connected bridgeless planar simple graphs with n vertices in which each internal face is a triangle.

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..200
• Ya-Ping Lu, Illustration of initial terms

Crossrefs

Row sums of A378103.

Cf. A005027 (2-connected), A342056 (3-connected), A378335 (sensed), A378339 (achiral), A378340.

Programs

PARI

A377785seq(30) \\ See PARI link in A378340 for program code.

Formula

a(n) = (A378335(n) + A378339(n))/2. - Andrew Howroyd, Nov 24 2024

Extensions

a(9) onwards from Andrew Howroyd, Nov 24 2024