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A384964 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of connected simple planar graphs with n nodes and k faces up to orientation preserving isomorphisms, n >= 1, k=1..max(1,2*n-4).

%I A384964 #8 Jun 15 2025 14:38:58
%S A384964 1,1,1,1,2,2,1,1,3,8,8,6,2,1,6,29,60,73,52,25,6,2,14,113,388,768,903,
%T A384964 728,379,136,26,6,34,444,2303,6584,11782,14321,12113,7298,3048,872,
%U A384964 147,17,95,1763,12650,49806,123547,210314,255884,228807,150929,73428,25536,6142,892,73
%N A384964 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of connected simple planar graphs with n nodes and k faces up to orientation preserving isomorphisms, n >= 1, k=1..max(1,2*n-4).
%C A384964 Equivalently, T(n,k) is the number of sensed simple planar maps with n vertices and k faces.
%C A384964 The number of edges is n+k-2.
%C A384964 Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 1..14 of this table.
%H A384964 Andrew Howroyd, <a href="/A384964/b384964.txt">Table of n, a(n) for n = 1..158</a> (rows 1..14)
%H A384964 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 19-22.
%e A384964 Triangle begins:
%e A384964    1;
%e A384964    1;
%e A384964    1,   1,
%e A384964    2,   2,    1,    1,
%e A384964    3,   8,    8,    6,     2,     1,
%e A384964    6,  29,   60,   73,    52,    25,     6,    2,
%e A384964   14, 113,  388,  768,   903,   728,   379,  136,   26,   6,
%e A384964   34, 444, 2303, 6584, 11782, 14321, 12113, 7298, 3048, 872, 147, 17;
%e A384964   ...
%Y A384964 Row sums are A384965.
%Y A384964 Antidiagonal sums are A006394.
%Y A384964 Columns 1..2 are A002995, A384966.
%Y A384964 Cf. A379430 (not necessarily simple), A342059 (2-connected), A239893 (3-connected), A384963 (unsensed).
%K A384964 nonn,tabf
%O A384964 1,5
%A A384964 _Andrew Howroyd_, Jun 13 2025