A006387 -id:A006387 - cp's OEIS frontend

A006385 Number of unsensed planar maps with n edges.

1, 2, 4, 14, 52, 248, 1416, 9172, 66366, 518868, 4301350, 37230364, 333058463, 3057319072, 28656583950, 273298352168, 2645186193457, 25931472185976, 257086490694917, 2574370590192556, 26010904915620261

Offset: 0

N. J. A. Sloane

The planar maps considered are connected and may contain loops and 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).
T. R. S. Walsh, personal communication.

Richard Kapolnai, Gabor Domokos, and Timea Szabo, Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes, Periodica Polytechnica Electrical Engineering, 56(1):11-10, 2012. Also arXiv:1206.1698, 2012. See Table 2.
Valery. A. Liskovets, A reductive technique for enumerating nonisomorphic planar maps, Discr. Math., v.156 (1996), 197-217.
Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps
Timothy R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3
Nicholas C. Wormald, Counting unrooted planar maps, Discrete Math. 36 (1981), no. 2, 205-225.

Antidiagonal sums of A277741.
Column k=0 of A379439.
Cf. A000168 (rooted), A006384 (sensed), A006443 (achiral), A006403 (2-connected), A090376.
Cf. A006387 (genus 1), A214814 (genus 2), A214815 (genus 3), A214816.

a(n) = (A006384(n) + A006443(n))/2. - Andrew Howroyd, Jan 13 2025

a(18)-a(19) added by Andrew Howroyd, Jan 13 2025

a(20) added by Andrew Howroyd, Jan 20 2025

A379439 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

Original entry on oeis.org

1, 2, 4, 1, 14, 6, 52, 40, 4, 248, 320, 76, 1416, 2946, 1395, 82, 9172, 29364, 24950, 4348, 66366, 309558, 427336, 160050, 7258, 518868, 3365108, 6987100, 4696504, 688976, 4301350, 37246245, 109761827, 118353618, 37466297, 1491629, 37230364, 416751008, 1668376886, 2675297588, 1512650776, 195728778

Offset: 0

Andrew Howroyd, Jan 16 2025

			Triangle begins:
  n\k     [0]      [1]      [2]      [3]     [4]
  [0]      1;
  [1]      2;
  [2]      4,       1;
  [3]     14,       6;
  [4]     52,      40,       4;
  [5]    248,     320,      76;
  [6]   1416,    2946,    1395,      82;
  [7]   9172,   29364,   24950,    4348;
  [8]  66366,  309558,  427336,  160050,   7258;
  [9] 518868, 3365108, 6987100, 4696504, 688976;

Andrew Howroyd, Table of n, a(n) for n = 0..120 (rows 0..20)
Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 4.

Row sums are A214816.
Columns 0..8 are A006385, A006387, A214814, A214815, A297880, A297881, A348798, A348800, A348801.
Cf. A269919 (rooted), A379438 (sensed), A380234 (achiral), A380235.

T(n,k) = (A379438(n,k) + A380234(n,k))/2.

A006386 Number of sensed genus 1 maps with n edges.

Original entry on oeis.org

1, 6, 46, 452, 4852, 52972, 587047, 6550808, 73483256, 827801468, 9360123740, 106189359544, 1208328304864, 13787042250528, 157700137398689, 1807893066408464, 20768681225892328, 239037464947999900, 2755989928117365244, 31826208029615881656, 368074022535205870382

Offset: 2

N. J. A. Sloane

A genus 1 map can be called a toroidal map.

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

T. D. Noe, Table of n, a(n) for n = 2..30 (from Mednykh and Nedela)
A. D. Mednykh and R. Nedela, Enumeration of unrooted maps with given genus, J. Combin. Th. B, 96 (2006), 706-729.
Timothy R. Walsh, Generating nonisomorphic maps without storing them, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 161-178.
Timothy R. Walsh, Counting maps on doughnuts, Theoretical Computer Science, vol.502, pp.4-15, (September-2013).
Timothy R. S. Walsh, Alain Giorgetti, Alexander Mednykh, Enumeration of unrooted orientable maps of arbitrary genus by number of edges and vertices, Discrete Math. 312 (2012), no. 17, 2660--2671. MR2935417. - From _N. J. A. Sloane_, Aug 01 2012

Column k=1 of A379438.

Cf. A006300 (rooted), A006384 (planar), A006387 (unsensed), A104595, A104596, A215019.

More terms from Valery A. Liskovets, Mar 22 2005

Edited by N. J. A. Sloane, May 23 2008

A214816 Number of unsensed combinatorial maps with n edges on an orientable surface of any genus.

Original entry on oeis.org

1, 2, 5, 20, 96, 644, 5839, 67834, 970568, 16256556, 308620966, 6506035400, 150358570914, 3775903806928, 102348067516576, 2977979542305736, 92579723269733557, 3062602106878957610, 107418879166917701583, 3981908920500346885116, 155550644128029095714786

Offset: 0

N. J. A. Sloane, Jul 31 2012

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..30
Antonio Breda d'Azevedo, Alexander Mednykh, and Roman Nedela, Enumeration of maps regardless of genus: Geometric approach, Discrete Mathematics, Volume 310, 2010, Pages 1184-1203.
Timothy R. Walsh, Space-efficient generation of nonisomorphic maps and hypermaps.
T. R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3.

Row sums of A379439.

Cf. A006385, A006387, A170946 (sensed), A170947 (achiral), A170948 (chiral pairs), A214814, A214815, A297880, A297881, A348798, A348800, A348801.

a(n) = (A170946(n) + A170947(n)) / 2. [Breda d'Azevedo, Mednykh & Nedela, Corollary 4.7] - Andrey Zabolotskiy, Jun 06 2024

a(12)-a(18) from Andrey Zabolotskiy, Jun 06 2024

a(19) onwards from Andrew Howroyd, Jan 27 2025

A214814 Number of unsensed genus 2 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 4, 76, 1395, 24950, 427336, 6987100, 109761827, 1668376886, 24689351504, 357467967214, 5083309341304, 71209097157108, 984963603696282, 13477371260785608, 182698708325667710, 2456600457435363198, 32796863046711248526

Offset: 0

N. J. A. Sloane, Jul 31 2012

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.
T. R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3

Column k=2 of A379439.
Cf. A006301 (rooted), A104595 (sensed).
Cf. A006385, A006387, A214815, A214816.

More terms from Evgeniy Krasko, Sep 17 2017

A214815 Number of unsensed genus 3 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 82, 4348, 160050, 4696504, 118353618, 2675297588, 55758114082, 1091344752470, 20318440463052, 363171011546210, 6275111078422480, 105369657960443204, 1726590417107274316, 27699670730854989616, 436246336648672487876

Offset: 0

N. J. A. Sloane, Jul 31 2012

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.
T. R. Walsh, Space-Efficient Generation of Nonisomorphic Maps and Hypermaps, J. Int. Seq. 18 (2015) # 15.4.3

Column k=3 of A379439.
Cf. A104742 (rooted), A104596 (sensed).
Cf. A006385, A006387, A214814, A214816.

More terms from Evgeniy Krasko, Sep 17 2017

A297880 Number of unsensed genus 4 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 7258, 688976, 37466297, 1512650776, 50355225387, 1461269893538, 38236656513725, 922552326544030, 20847359639841664, 446290728182323620, 9129236228868478458, 179639607187998993180, 3418366706444416598777

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=4 of A379439.
Cf. A215402 (rooted), A215019 (sensed).
Cf. A006385, A006387, A214814, A214815, A214816.

a(20) added by Andrew Howroyd, Jan 20 2025

A348798 a(n) = number of unsensed genus 6 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 506855279, 84930743344, 7601322881752, 482475325333252, 24347701836204379, 1038820801135250668, 38928478953655850016, 1314623638623845390906, 40749347642026348171659

Offset: 0

Michael De Vlieger, Nov 01 2021

nonn

Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 3.

Column k=6 of A379439.
Cf. A238356 (rooted), A239919 (sensed).
Cf. A006387, A214814, A214815, A297880, A297881, A348800, A348801.

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.

A348800 a(n) = number of unsensed genus 7 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254118439668, 52148049818864, 5634797561708385, 426497331688178676, 25388940147173859412, 1265623233919838264624, 54940200059090328012148

Offset: 0

Michael De Vlieger, Nov 01 2021

nonn

Evgeniy Krasko and Alexander Omelchenko, Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus, arXiv:1712.10139 [math.CO], 2017, see Appendix Table 3.

Column k=7 of A379439.
Cf. A238357 (rooted), A239921 (sensed).
Cf. A006387, A214814, A214815, A297880, A297881, A348798, A348801.

cp's OEIS Frontend

A006385 Number of unsensed planar maps with n edges.

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A379439 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

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A006386 Number of sensed genus 1 maps with n edges.

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A214816 Number of unsensed combinatorial maps with n edges on an orientable surface of any genus.

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A214814 Number of unsensed genus 2 maps with n edges.

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A214815 Number of unsensed genus 3 maps with n edges.

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A297880 Number of unsensed genus 4 maps with n edges.

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A348798 a(n) = number of unsensed genus 6 maps with n edges.

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A297881 Number of unsensed genus 5 maps with n edges.

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A348800 a(n) = number of unsensed genus 7 maps with n edges.

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