A377785 - OEIS

%I #24 Nov 25 2024 16:29:08

%S 1,2,5,19,80,407,2403,15570,107366,773660,5746826,43693041,338367370,

%T 2660629311,21193182914,170714892489,1388711749891,11395477091396,

%U 94238431709661,784796579069288,6576997589788217,55435506835745851,469698698872829672,3998806331800289798

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

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

%C The planar maps considered are without loops or isthmuses.

%C 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.

%H Andrew Howroyd, <a href="/A377785/b377785.txt">Table of n, a(n) for n = 3..200</a>

%H Ya-Ping Lu, <a href="/A377785/a377785.pdf">Illustration of initial terms</a>

%F a(n) = (A378335(n) + A378339(n))/2. - _Andrew Howroyd_, Nov 24 2024

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

%Y Row sums of A378103.

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

%K nonn,new

%O 3,2

%A _Ya-Ping Lu_, Nov 06 2024

%E a(9) onwards from _Andrew Howroyd_, Nov 24 2024