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A384963 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, n >= 1, k=1..max(1,2*n-4).

%I A384963 #10 Jun 15 2025 14:39:09
%S A384963 1,1,1,1,2,2,1,1,3,7,7,5,2,1,6,22,42,49,35,18,5,2,12,76,237,442,510,
%T A384963 412,218,84,18,5,27,271,1293,3539,6205,7482,6318,3833,1623,485,88,14,
%U A384963 65,1001,6757,25842,63254,106985,129782,115988,76582,37421,13111,3228,489,50
%N A384963 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, n >= 1, k=1..max(1,2*n-4).
%C A384963 Equivalently, T(n,k) is the number of unsensed simple planar maps with n vertices and k faces.
%C A384963 The number of edges is n+k-2.
%C A384963 Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 1..14 of this table.
%H A384963 Andrew Howroyd, <a href="/A384963/b384963.txt">Table of n, a(n) for n = 1..158</a> (rows 1..14)
%H A384963 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 A384963 Triangle begins:
%e A384963    1;
%e A384963    1;
%e A384963    1,   1;
%e A384963    2,   2,    1,    1,
%e A384963    3,   7,    7,    5,    2,    1;
%e A384963    6,  22,   42,   49,   35,   18,    5,    2;
%e A384963   12,  76,  237,  442,  510,  412,  218,   84,   18,   5;
%e A384963   27, 271, 1293, 3539, 6205, 7482, 6318, 3833, 1623, 485, 88, 14;
%e A384963   ...
%Y A384963 Row sums are A372892.
%Y A384963 Antidiagonal sums are A006395.
%Y A384963 Columns 1..2 are A006082, A384967.
%Y A384963 Cf. A277741 (not necessarily simple), A342060 (2-connected), A212438 (3-connected), A384850 (version by number of edges then vertices), A384964 (sensed version).
%K A384963 nonn,tabf
%O A384963 1,5
%A A384963 _Andrew Howroyd_, Jun 13 2025