cp's OEIS Frontend

A342059 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.

%I A342059 #11 Mar 28 2021 14:23:56
%S A342059 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 A342059 87,576,2128,4009,4055,2332,804,147,17,1,7,161,1664,9659,31252,59244,
%U A342059 66289,46521,20604,5743,892,73,1,9,286,4151,34700,168757,505410,952044,1156127,931227,506318,183980,43180,5876,389
%N A342059 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 A342059 The number of edges is n+k-2.
%C A342059 Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 3..15 of this table.
%H A342059 Andrew Howroyd, <a href="/A342059/b342059.txt">Table of n, a(n) for n = 3..171</a> (rows 3..15)
%H A342059 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 A342059 T(n,2) = 1.
%F A342059 T(n,3) = A253186(n-2).
%e A342059 Triangle begins:
%e A342059   1;
%e A342059   1, 1,  1;
%e A342059   1, 2,  5,   2,    1;
%e A342059   1, 3, 17,  31,   22,    6,    2;
%e A342059   1, 4, 42, 157,  318,  265,  123,   26,   6;
%e A342059   1, 6, 87, 576, 2128, 4009, 4055, 2332, 804, 147, 17;
%e A342059   ...
%Y A342059 Row sums are A342058.
%Y A342059 Cf. A006406 (by edges), A239893 (3-connected), A342060.
%K A342059 nonn,tabf
%O A342059 3,6
%A A342059 _Andrew Howroyd_, Mar 27 2021