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A378077 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of planar graphs with n vertices and k faces having connectivity exactly 2 and minimum vertex degree at least 3, k=6..2n-5.

%I A378077 #8 Nov 15 2024 19:38:51
%S A378077 1,1,1,3,7,2,1,8,35,60,47,12,0,5,72,307,647,652,325,59,0,3,86,776,
%T A378077 3395,7647,9582,6654,2442,368,0,0,45,1041,9091,38876,94278,136628,
%U A378077 121204,64232,18916,2363,0,0,18,827,14407,111076,468211,1192511,1937266,2049784,1409199,607746,150161,16253
%N A378077 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of planar graphs with n vertices and k faces having connectivity exactly 2 and minimum vertex degree at least 3, k=6..2n-5.
%C A378077 The graphs are 2-connected, but not 3-connected. Graphs with minimum degree at least 3 are also called homeomorphically irreducible.
%C A378077 The number of edges is n + k - 2.
%H A378077 Andrew Howroyd, <a href="/A378077/b378077.txt">Table of n, a(n) for n = 6..95</a> (rows 6..14)
%F A378077 T(n,k) = A212438(n,k) - A378075(n,k).
%e A378077 Triangle begins:
%e A378077   n\k| 6  7   8     9    10     11     12      13      14     15     16    17
%e A378077 -----+------------------------------------------------------------------------
%e A378077    6 | 1, 1;
%e A378077    7 | 1, 3,  7,    2;
%e A378077    8 | 1, 8, 35,   60,   47,    12;
%e A378077    9 | 0, 5, 72,  307,  647,   652,   325,     59;
%e A378077   10 | 0, 3, 86,  776, 3395,  7647,  9582,   6654,   2442,   368;
%e A378077   11 | 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363;
%e A378077   ...
%Y A378077 Rows sums are A187927.
%Y A378077 Antidiagonals sums give A187928.
%Y A378077 Cf. A378075.
%K A378077 nonn,tabf
%O A378077 6,4
%A A378077 _Andrew Howroyd_, Nov 15 2024