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

3,2

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

Formula

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

Prog

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

Crossrefs

Row sums of A378103.

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

Sequence in context: A222055 A228569 A204328 * A288911 A138911 A181513

Adjacent sequences: A377782 A377783 A377784 * A377786 A377787 A377788

Keyword

nonn,new

Author

Ya-Ping Lu, Nov 06 2024

Extensions

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

Status

approved