A006385 -id:A006385 - cp's OEIS frontend

A006403 Number of unsensed 2-connected planar maps with n edges.

0, 1, 2, 3, 6, 15, 36, 114, 396, 1565, 6756, 31563, 154370, 785113, 4099948, 21870704, 118624544, 652485364, 3631820462, 20426666644, 115949791342, 663640383400, 3826858500878, 22218232389849, 129802836253994

Offset: 1

N. J. A. Sloane

nonn

The maps considered here may include parallel edges. - Andrew Howroyd, Jan 13 2025

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Timothy R. Walsh, personal communication.

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
Timothy R. Walsh, Number of sensed planar maps with n edges and m vertices, p. 41.

Row sums of A379432.

Cf. A000139 (rooted), A006385, A006402 (sensed), A006407 (without parallel edges), A006444 (achiral).

a(n) = (A006402(n) + A006444(n))/2. - Andrew Howroyd, Jan 13 2025

a(23)-a(25) added by Andrew Howroyd, Jan 13 2025

A297881 Number of unsensed genus 5 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1491629, 195728778, 14019733828, 724646387874, 30220873171570, 1079253898643492, 34231899372185491, 988157793188200998, 26412878913430197293, 662133032168309300424, 15719783014093104131694

Offset: 0

Evgeniy Krasko, Jan 07 2018

nonn

Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017.
Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps.

Column k=5 of A379439.
Cf. A238355 (rooted), A239918 (sensed).
Cf. A006385, A006387, A214814, A214815, A214816, A297880.

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

N. J. A. Sloane

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

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Row sums of A384850, antidiagonal sums of A384963.

Cf. A006385, A006391, A006394 (sensed), A022558 (rooted), A372892 (with n vertices).

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

A006391 Number of unsensed loopless planar maps with n edges.

Original entry on oeis.org

1, 1, 2, 5, 14, 45, 191, 871, 4682, 27336, 172706, 1150322, 7989004

Offset: 0

N. J. A. Sloane

nonn

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A000260 (rooted), A006390 (sensed).

a(8)-a(12) from Sean A. Irvine, Mar 29 2017

a(0)=1 prepended by Andrew Howroyd, Jan 14 2025

A006405 Number of unsensed 2-connected maps with n edges and without faces of degree 2.

Original entry on oeis.org

1, 1, 2, 5, 9, 24, 70, 222, 785, 3055

Offset: 3

N. J. A. Sloane

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A006403, A006405 (sensed).

a(11) and a(12) from Sean A. Irvine, Apr 02 2017

A006393 Number of unsensed planar maps with n edges and without faces of degree 1 or 2.

Original entry on oeis.org

1, 0, 1, 4, 9, 32, 132, 597, 3064, 17114, 102274, 643907, 4219540

Offset: 0

N. J. A. Sloane

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A006389, A006392 (sensed), A379434 (rooted).

a(8)-a(12) from Sean A. Irvine, Mar 29 2017

a(0)-a(1) prepended by Andrew Howroyd, Jan 16 2025

A006397 Number of unsensed planar maps with n edges and without faces or vertices of degree 1.

Original entry on oeis.org

1, 0, 1, 2, 4, 10, 34, 114, 475, 2104, 10177, 52012, 279874

Offset: 0

N. J. A. Sloane

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A006389, A006396 (sensed), A379435 (rooted).

a(9)-a(12) from Sean A. Irvine, Mar 28 2017

a(0)-a(2) prepended by Andrew Howroyd, Jan 16 2025

A006401 Number of unsensed simple planar maps with n edges and without vertices of degree 1.

Original entry on oeis.org

1, 0, 0, 1, 1, 2, 5, 10, 28, 86, 285, 1055, 4211

Offset: 0

N. J. A. Sloane

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

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A006389, A006395, A006400 (sensed), A379436 (rooted).

a(11)-a(12) from Sean A. Irvine, Mar 31 2017

a(0)-a(2) prepended by Andrew Howroyd, Jan 16 2025

A006399 Number of unsensed planar maps with n edges and without loops or isthmuses.

Original entry on oeis.org

1, 0, 1, 2, 4, 8, 27, 76, 295, 1188, 5462, 26580, 138110

Offset: 0

N. J. A. Sloane

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

Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.

Cf. A006385, A006391, A006398 (sensed), A099553 (rooted).

a(9)-a(12) from Sean A. Irvine, Mar 29 2017

a(0)-a(1) prepended by Andrew Howroyd, Jan 16 2025

A090376 Number of rooted generalized quadrangular dissections of weight n of a closed disk: planar maps having the external face bounded by a polygon and all internal faces of size 4.

Original entry on oeis.org

1, 4, 15, 80, 362, 1832, 8994, 46384, 238838, 1257824

Offset: 0

Valery A. Liskovets, Dec 03 2003

Some boundary mutually non-adjacent nodes of valency 2 are marked as singular; (boundary) edges incident to them are also called singular. The maps are considered up to rotations and reflections. Rooting means distinguishing a non-singular edge, an end and an internal side of it. n is the number of internal edges plus half of the number of non-singular boundary edges.

No formula is known. For any generalized quadrangular dissection, s==n (mod 2), where s is the number of singular nodes.

			The four rooted generalized quadrangular dissections of weight 1 are
...................____......____..
.X<---X..X---<X.../....\..../....\.
.|....|..|....|..X<--X..O..X--<X..O
.|....|..|....|...\____/....\____/.
.X----O..X----O....................
where O is the singular node and -> is the rooted edge-end.

V. A. Liskovets, A reductive technique for enumerating nonisomorphic planar maps, Discr. Math., v.156 (1996), 197-217.

Cf. A006385.

cp's OEIS Frontend

A006403 Number of unsensed 2-connected planar maps with n edges.

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A297881 Number of unsensed genus 5 maps with n edges.

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

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A006391 Number of unsensed loopless planar maps with n edges.

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A006405 Number of unsensed 2-connected maps with n edges and without faces of degree 2.

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A006393 Number of unsensed planar maps with n edges and without faces of degree 1 or 2.

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A006397 Number of unsensed planar maps with n edges and without faces or vertices of degree 1.

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A006401 Number of unsensed simple planar maps with n edges and without vertices of degree 1.

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A006399 Number of unsensed planar maps with n edges and without loops or isthmuses.

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A090376 Number of rooted generalized quadrangular dissections of weight n of a closed disk: planar maps having the external face bounded by a polygon and all internal faces of size 4.

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