A348801 -id:A348801 - cp's OEIS frontend

A238358 Number of genus-8 rooted maps with n edges.

11288163762500625, 2927974178219879250, 394372363395179602125, 36751560969705187643982, 2663973075006196131775590, 160098273686603663417293308, 8303278159618015743881266599, 381958851175370643701603049354, 15896435050196091382215375181044, 607566907750822335161584110201960

Offset: 16

Joerg Arndt, Feb 26 2014

nonn

Andrew Howroyd, Table of n, a(n) for n = 16..200
Sean R. Carrell and Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], (19-March-2014).
Gheorghe Coserea, The g.f. as a rational function of y=A005159(x)
Steven R. Finch, An exceptional convolutional recurrence, arXiv:2408.12440 [math.CO], 22 Aug 2024.

Column g=8 of A269919.
Cf. A239922 (unrooted sensed), A348801 (unrooted unsensed).
Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, A238357, this sequence, A238359, A238360.

T[0, 0] = 1; T[n_, g_] /; g < 0 || g > n/2 = 0; T[n_, g_] := T[n, g] = ((4 n - 2)/3 T[n - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 T[n - 2, g - 1] + 1/2 Sum[(2 k - 1) (2 (n - k) - 1) T[k - 1, i] T[n - k - 1, g - i], {k, 1, n - 1}, {i, 0, g}])/((n + 1)/6);
a[n_] := T[n, 8];
Table[a[n], {n, 16, 30}] (* Jean-François Alcover, Jul 20 2018 *)

PARI
```
\\ see A238396
```

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.

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

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.

A239922 Number of unrooted maps with n edges of (orientable) genus 8.

Original entry on oeis.org

352755124921122, 86116887841273186, 10954787876407932816, 967146341367928365308, 66599326875830666763353, 3811863659211606517416928, 188710867264106506704457217, 8303453286421604392505856232, 331175730212422476849562734689, 12151338155016475304016716988472

Offset: 16

Alain Giorgetti, Mar 29 2014

nonn

Andrew Howroyd, Table of n, a(n) for n = 16..60
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.

Column k=8 of A379438.
Cf. A238358 (rooted), A348801 (unsensed).
Cf. A006386, A104595, A104596, A215019, A239918, A239919, A239921.

a(24) onwards added by Andrew Howroyd, Jan 18 2025

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

A238358 Number of genus-8 rooted maps with n edges.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

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).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

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

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

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

Views

Author

Keywords

Links

Crossrefs

A239922 Number of unrooted maps with n edges of (orientable) genus 8.

Views

Author

Keywords

Links

Crossrefs

Extensions

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

Views

Author

Keywords

Links

Crossrefs