A297880 -id:A297880 - cp's OEIS frontend

A215402 Number of rooted maps of (orientable) genus 4 containing n edges.

225225, 24635754, 1495900107, 66519597474, 2416610807964, 75981252764664, 2141204115631518, 55352670009315660, 1334226671709010578, 30347730709395639732, 657304672067357799042, 13652607304062788395788, 273469313030628783700080, 5306599156694095573465824, 100128328831437989131706976, 1842794650155970906232185656

Offset: 8

Alain Giorgetti, Aug 09 2012

nonn

Andrew Howroyd, Table of n, a(n) for n = 8..500
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], (19-March-2014).
Steven R. Finch, An exceptional convolutional recurrence, arXiv:2408.12440 [math.CO], 22 Aug 2024.
Alexander Mednykh, Alain Giorgetti, Enumeration of genus four maps by number of edges, Ars Mathematica Contemporanea 4 (2011), 351--361.

Row sums of A269924.
Column g=4 of A269919.
Cf. A215019 (unrooted sensed maps), A297880 (unrooted unsensed maps).
Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, this sequence, A238355, A238356, A238357, 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, 4];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, Jul 20 2018 *)

A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A215402_ser(N) = {
  my(y=A005159_ser(N+1));
  -y*(y-1)^8*(15812*y^12 - 189744*y^11 + 4708549*y^10 - 24892936*y^9 + 173908449*y^8 - 567987942*y^7 + 1743939189*y^6 - 3485359548*y^5 + 5448471852*y^4 - 6051484928*y^3 + 4633500336*y^2 - 2228416192*y + 517976128)/(81*(y-2)^17*(y+2)^10);
};
Vec(A215402_ser(16)) \\ Gheorghe Coserea, Jun 02 2017

More terms from Joerg Arndt, Feb 26 2014

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

A215019 Number of unrooted maps with n edges of (orientable) genus 4.

Original entry on oeis.org

14118, 1369446, 74803564, 3023693380, 100692692173, 2922359760376, 76471600288836, 1845089145736960, 41694584320696782, 892580319444417876, 18258463136626650660, 359279139700128276168, 6836732826365623258492, 126347598971804884131800, 2275643837092089686415858

Offset: 8

N. J. A. Sloane, Aug 01 2012

nonn

Andrew Howroyd, Table of n, a(n) for n = 8..45
Alexander Mednykh, Alain Giorgetti, Enumeration of genus four maps by number of edges. Ars Mathematica Contemporanea 4 (2011), 351-361. MR2842107
A. D. Mednykh and R. Nedela, Enumeration of unrooted maps with given genus, preprint (submitted to J. Combin. Th. B).
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=4 of A379438.
Cf. A215402 (rooted), A297880 (unsensed).
Cf. A006386, A104595, A104596 (genus 3), A239918 (genus 5), A239919 (genus 6).

a(12) 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.

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.

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

A215402 Number of rooted maps of (orientable) genus 4 containing 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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A215019 Number of unrooted maps with n edges of (orientable) genus 4.

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

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