cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A378076 Number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n edges.

Original entry on oeis.org

1, 0, 1, 2, 3, 6, 16, 37, 100, 293, 888, 2822, 9305, 31274, 106972, 370828, 1298058, 4582413, 16289759, 58259600, 209465186
Offset: 6

Views

Author

Andrew Howroyd, Nov 15 2024

Keywords

Comments

Homeomorphically irreducible means each vertex has a degree of at least 3.

Crossrefs

Antidiagonal sums of A378075.

Formula

a(n) = A002840(n) + A187928(n).
a(n) = Sum_{k=4..n-2} A378075(k, n+2-k).

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.

Original entry on oeis.org

1, 1, 1, 3, 7, 2, 1, 8, 35, 60, 47, 12, 0, 5, 72, 307, 647, 652, 325, 59, 0, 3, 86, 776, 3395, 7647, 9582, 6654, 2442, 368, 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363, 0, 0, 18, 827, 14407, 111076, 468211, 1192511, 1937266, 2049784, 1409199, 607746, 150161, 16253
Offset: 6

Views

Author

Andrew Howroyd, Nov 15 2024

Keywords

Comments

The graphs are 2-connected, but not 3-connected. Graphs with minimum degree at least 3 are also called homeomorphically irreducible.
The number of edges is n + k - 2.

Examples

			Triangle begins:
  n\k| 6  7   8     9    10     11     12      13      14     15     16    17
-----+------------------------------------------------------------------------
   6 | 1, 1;
   7 | 1, 3,  7,    2;
   8 | 1, 8, 35,   60,   47,    12;
   9 | 0, 5, 72,  307,  647,   652,   325,     59;
  10 | 0, 3, 86,  776, 3395,  7647,  9582,   6654,   2442,   368;
  11 | 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363;
  ...
		

Crossrefs

Rows sums are A187927.
Antidiagonals sums give A187928.
Cf. A378075.

Formula

T(n,k) = A212438(n,k) - A378075(n,k).

A378074 Number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n nodes.

Original entry on oeis.org

0, 0, 0, 1, 2, 9, 47, 420, 4673, 63253, 927238, 14342093, 229607392, 3776227106, 63482545872, 1087322656758, 18927037827561
Offset: 1

Views

Author

Andrew Howroyd, Nov 15 2024

Keywords

Comments

Homeomorphically irreducible means each vertex has a degree of at least 3.

Crossrefs

Row sums of A378075.

Formula

a(n) = A000944(n) + A187927(n).
Showing 1-3 of 3 results.