A239922 -id:A239922 - 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
```

A379438 Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

Original entry on oeis.org

1, 2, 4, 1, 14, 6, 57, 46, 4, 312, 452, 106, 2071, 4852, 2382, 131, 15030, 52972, 46680, 8158, 117735, 587047, 830848, 313611, 14118, 967850, 6550808, 13804864, 9326858, 1369446, 8268816, 73483256, 218353000, 236095958, 74803564, 2976853, 72833730, 827801468, 3328822880, 5345316004, 3023693380, 391288854

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]     57,      46,        4;
  [5]    312,     452,      106;
  [6]   2071,    4852,     2382,     131;
  [7]  15030,   52972,    46680,    8158;
  [8] 117735,  587047,   830848,  313611,   14118;
  [9] 967850, 6550808, 13804864, 9326858, 1369446;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..120 (rows 0..20)
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, Alain Giorgetti, and 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.

Row sums are A170946.
Columns 0..10 are A006384, A006386, A104595, A104596, A215019, A239918, A239919, A239921, A239922, A239923, A239924.
Cf. A269919 (rooted), A379439 (unsensed), A380234 (achiral), A380235.

A348801 a(n) = number of unsensed genus 8 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176377605783906, 43058445711817178, 5477393987229533288, 483573171728920541590, 33299663456795126129156

Offset: 0

Michael De Vlieger, Nov 01 2021

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.

Column k=8 of A379439.
Cf. A238358 (rooted), A239922 (sensed).
Cf. A006387, A214814, A214815, A297880, A297881, A348798, A348800.

A239923 Number of unrooted maps with n edges of (orientable) genus 9.

Original entry on oeis.org

324039613564554401, 92075738368876748710, 13524920870667446819490, 1368913666872922446728390, 107367565606418008964576338, 6957847952983327441248445908, 387883525432376769353915075571

Offset: 18

Alain Giorgetti, Mar 29 2014

nonn

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=9 of A379438.
Cf. A238359 (rooted).
Cf. A006386, A104595, A104596, A215019, A239918, A239919, A239921, A239922.

A239924 Number of unrooted maps with n edges of (orientable) genus 10.

Original entry on oeis.org

380751174738424280720, 123800701289478148878890, 20679270860399513431761798, 2366561529248819497695971912, 208773430159079852919281433050, 15143758135416335992767275804168, 940742579115450773885994408739386

Offset: 20

Alain Giorgetti, Mar 29 2014

nonn

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=10 of A379438.
Cf. A238360 (rooted).
Cf. A006386, A104595, A104596, A215019, A239918, A239919, A239921, A239922, A239923.

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

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A379438 Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and genus k, 0 <= k <= floor(n/2).

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A348801 a(n) = number of unsensed genus 8 maps with n edges.

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A239923 Number of unrooted maps with n edges of (orientable) genus 9.

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A239924 Number of unrooted maps with n edges of (orientable) genus 10.

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