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 1-4 of 4 results.

A006395 Number of unsensed planar maps with n edges and without loops or parallel edges.

Original entry on oeis.org

1, 1, 1, 3, 5, 14, 42, 150, 624, 2947, 15079, 82607, 474030, 2816952, 17194524, 107226255
Offset: 0

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Author

Keywords

Comments

The planar maps considered here are connected. A planar map without loops or parallel edges is called simple.

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Row sums of A384850, antidiagonal sums of A384963.
Cf. A006385, A006391, A006394 (sensed), A022558 (rooted), A372892 (with n vertices).

Extensions

a(9)-a(12) from Sean A. Irvine, Mar 30 2017
a(0)=1 prepended by Andrew Howroyd, Jan 16 2025
a(13)-a(15) added by Andrew Howroyd, Jun 15 2025

A384964 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of connected simple planar graphs with n nodes and k faces up to orientation preserving isomorphisms, n >= 1, k=1..max(1,2*n-4).

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 1, 3, 8, 8, 6, 2, 1, 6, 29, 60, 73, 52, 25, 6, 2, 14, 113, 388, 768, 903, 728, 379, 136, 26, 6, 34, 444, 2303, 6584, 11782, 14321, 12113, 7298, 3048, 872, 147, 17, 95, 1763, 12650, 49806, 123547, 210314, 255884, 228807, 150929, 73428, 25536, 6142, 892, 73
Offset: 1

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Author

Andrew Howroyd, Jun 13 2025

Keywords

Comments

Equivalently, T(n,k) is the number of sensed simple planar maps with n vertices and k faces.
The number of edges is n+k-2.
Terms of this sequence can be computed using the tool "plantri". The expanded reference gives rows 1..14 of this table.

Examples

			Triangle begins:
   1;
   1;
   1,   1,
   2,   2,    1,    1,
   3,   8,    8,    6,     2,     1,
   6,  29,   60,   73,    52,    25,     6,    2,
  14, 113,  388,  768,   903,   728,   379,  136,   26,   6,
  34, 444, 2303, 6584, 11782, 14321, 12113, 7298, 3048, 872, 147, 17;
  ...
		

Crossrefs

Row sums are A384965.
Antidiagonal sums are A006394.
Columns 1..2 are A002995, A384966.
Cf. A379430 (not necessarily simple), A342059 (2-connected), A239893 (3-connected), A384963 (unsensed).

A006400 Number of sensed simple planar maps with n edges and without vertices of degree 1.

Original entry on oeis.org

1, 0, 0, 1, 1, 2, 5, 11, 33, 117, 431, 1755, 7485
Offset: 0

Views

Author

Keywords

Comments

A simple planar map is a planar map without loops or parallel edges. - Andrew Howroyd, Jan 16 2025

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006384, A006388, A006394, A006401 (unsensed), A379436 (rooted).

Extensions

a(11) and a(12) from Sean A. Irvine, Mar 30 2017
a(0)-a(2) prepended by Andrew Howroyd, Jan 14 2025

A384965 Number of sensed simple planar maps with n vertices.

Original entry on oeis.org

1, 1, 2, 6, 28, 253, 3461, 58963, 1139866, 23952568, 534729502, 12511055327, 303919972592, 7613826460120
Offset: 1

Views

Author

Andrew Howroyd, Jun 13 2025

Keywords

Comments

A simple planar map is a planar map without loops or parallel edges.

Crossrefs

Row sums of A384964.
Cf. A006394 (with n edges), A372892 (unsensed version).
Showing 1-4 of 4 results.