A342059 - OEIS

%I #11 Mar 28 2021 14:23:56

%S 1,1,1,1,1,2,5,2,1,1,3,17,31,22,6,2,1,4,42,157,318,265,123,26,6,1,6,

%T 87,576,2128,4009,4055,2332,804,147,17,1,7,161,1664,9659,31252,59244,

%U 66289,46521,20604,5743,892,73,1,9,286,4151,34700,168757,505410,952044,1156127,931227,506318,183980,43180,5876,389

%N Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected planar graphs with n nodes and k faces up to orientation preserving isomorphisms, n >= 3, k=2..2*n-4.

%C The number of edges is n+k-2.

%C Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 3..15 of this table.

%H Andrew Howroyd, <a href="/A342059/b342059.txt">Table of n, a(n) for n = 3..171</a> (rows 3..15)

%H Gunnar Brinkmann and Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/papers/plantri-full.pdf">Fast generation of planar graphs (expanded edition)</a>, Tables 23-26.

%F T(n,2) = 1.

%F T(n,3) = A253186(n-2).

%e Triangle begins:

%e   1;

%e   1, 1,  1;

%e   1, 2,  5,   2,    1;

%e   1, 3, 17,  31,   22,    6,    2;

%e   1, 4, 42, 157,  318,  265,  123,   26,   6;

%e   1, 6, 87, 576, 2128, 4009, 4055, 2332, 804, 147, 17;

%e   ...

%Y Row sums are A342058.

%Y Cf. A006406 (by edges), A239893 (3-connected), A342060.

%K nonn,tabf

%O 3,6

%A _Andrew Howroyd_, Mar 27 2021