A348800 -id:A348800 - cp's OEIS frontend

A238357 Number of genus-7 rooted maps with n edges.

14230536445125, 3128879373858000, 360626952084151500, 29001816720933903504, 1828003659229082834100, 96187365300257285300064, 4395215998078319892167640, 179153431308203084149883760, 6641365771586560905099092466, 227189907562197156785567456832, 7252879937219595844346639732688

Offset: 14

Joerg Arndt, Feb 26 2014

nonn

Andrew Howroyd, Table of n, a(n) for n = 14..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=7 of A269919.
Cf. A239921 (unrooted sensed), A348800 (unrooted unsensed).
Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, A238356, this sequence, A238358, 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, 7];
Table[a[n], {n, 14, 30}] (* Jean-François Alcover, Jul 20 2018 *)

PARI
```
\\ see A238396
```

system("wget http://oeis.org/A238357/a238357.txt");
A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A238357_ser(N) = subst(read("a238357.txt"), 'y, A005159_ser(N+14));
Vec(A238357_ser(11)) \\ Gheorghe Coserea, Jun 03 2017

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

A239921 Number of unrooted maps with n edges of (orientable) genus 7.

Original entry on oeis.org

508233789579, 104295987346126, 11269592389125547, 852994611088758224, 50777879440443305426, 2531246455428148382456, 109880399953287962099588, 4265557888300762164284822, 150940131172496245801920542, 4938911033961317567088755908, 151101665358744941452325232448

Offset: 14

Alain Giorgetti, Mar 29 2014

nonn

Andrew Howroyd, Table of n, a(n) for n = 14..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=7 of A379438.
Cf. A238357 (rooted), A348800 (unsensed).
Cf. A006386, A104595, A104596, A215019, A239918, A239919.

a(23) onwards added by Andrew Howroyd, Jan 18 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.

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.

cp's OEIS Frontend

A238357 Number of genus-7 rooted 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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A214816 Number of unsensed combinatorial maps with n edges on an orientable surface of any genus.

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A239921 Number of unrooted maps with n edges of (orientable) genus 7.

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

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

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