A378074 -id:A378074 - cp's OEIS frontend

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.

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, 13, 146, 603, 1280, 1420, 883, 278, 50, 0, 0, 0, 8, 162, 1409, 6030, 13781, 18404, 14570, 6884, 1772, 233, 0, 0, 0, 0, 83, 1809, 15225, 64502, 158717, 240841, 233286, 144005, 55444, 12077, 1249

Offset: 4

Andrew Howroyd, Nov 15 2024

The number of edges is n + k - 2.

			Triangle begins:
  n\k| 4  5  6   7    8     9    10     11     12     13    14    15   16
-----+--------------------------------------------------------------------
   4 | 1;
   5 | 0, 1, 1;
   6 | 0, 1, 3,  3,   2;
   7 | 0, 0, 3, 11,  18,   10,    5;
   8 | 0, 0, 3, 19,  77,  134,  123,    50,    14;
   9 | 0, 0, 0, 13, 146,  603, 1280,  1420,   883,   278,   50;
  10 | 0, 0, 0,  8, 162, 1409, 6030, 13781, 18404, 14570, 6884, 1772, 233;
  ...

Andrew Howroyd, Table of n, a(n) for n = 4..124 (rows 4..14)

Row sums are A378074.
Antidiagonal sums give A378076.
Cf. A212438, A342060, A378077.

T(n,k) = A212438(n,k) + A378077(n,k).

cp's OEIS Frontend

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.

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