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

4,7

Comments

The number of edges is n + k - 2.

Links

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

Formula

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

Example

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;
  ...

Crossrefs

Row sums are A378074.

Antidiagonal sums give A378076.

Cf. A212438, A342060, A378077.

Sequence in context: A053375 A117252 A332498 * A181407 A114187 A016037

Adjacent sequences: A378072 A378073 A378074 * A378076 A378077 A378078

Keyword

nonn,tabf

Author

Andrew Howroyd, Nov 15 2024

Status

approved