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A378075 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n nodes and k faces, k=4..2n-4.

%I A378075 #11 Nov 15 2024 19:39:01
%S A378075 1,0,1,1,0,1,3,3,2,0,0,3,11,18,10,5,0,0,3,19,77,134,123,50,14,0,0,0,
%T A378075 13,146,603,1280,1420,883,278,50,0,0,0,8,162,1409,6030,13781,18404,
%U A378075 14570,6884,1772,233,0,0,0,0,83,1809,15225,64502,158717,240841,233286,144005,55444,12077,1249
%N A378075 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n nodes and k faces, k=4..2n-4.
%C A378075 The number of edges is n + k - 2.
%H A378075 Andrew Howroyd, <a href="/A378075/b378075.txt">Table of n, a(n) for n = 4..124</a> (rows 4..14)
%F A378075 T(n,k) = A212438(n,k) + A378077(n,k).
%e A378075 Triangle begins:
%e A378075   n\k| 4  5  6   7    8     9    10     11     12     13    14    15   16
%e A378075 -----+--------------------------------------------------------------------
%e A378075    4 | 1;
%e A378075    5 | 0, 1, 1;
%e A378075    6 | 0, 1, 3,  3,   2;
%e A378075    7 | 0, 0, 3, 11,  18,   10,    5;
%e A378075    8 | 0, 0, 3, 19,  77,  134,  123,    50,    14;
%e A378075    9 | 0, 0, 0, 13, 146,  603, 1280,  1420,   883,   278,   50;
%e A378075   10 | 0, 0, 0,  8, 162, 1409, 6030, 13781, 18404, 14570, 6884, 1772, 233;
%e A378075   ...
%Y A378075 Row sums are A378074.
%Y A378075 Antidiagonal sums give A378076.
%Y A378075 Cf. A212438, A342060, A378077.
%K A378075 nonn,tabf
%O A378075 4,7
%A A378075 _Andrew Howroyd_, Nov 15 2024