A380235 -id:A380235 - cp's OEIS frontend

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).

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.

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.

A348802 a(n) = number of non-orientable genus 1 maps with n edges.

Original entry on oeis.org

0, 1, 4, 19, 106, 709, 5356, 44558, 397146, 3716039, 35967272, 356784008, 3605014966, 36955965852, 383320824698

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 5.

Column k=1 of A380235.

Cf. A348803, A348804, A348805, A348806, A348807, A348808, A348809, A348810, A348811.

A348803 a(n) = number of non-orientable genus 2 maps with n edges.

Original entry on oeis.org

0, 0, 2, 16, 137, 1254, 12597, 133518, 1464725, 16373700, 185086459, 2106417804, 24081813881, 276231542440, 3176840637522

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 5.

Column k=2 of A380235.

Cf. A348802, A348804, A348805, A348806, A348807, A348808, A348809, A348810, A348811.

A348804 a(n) = number of non-orientable genus 3 maps with n edges.

Original entry on oeis.org

0, 0, 0, 8, 128, 1890, 27036, 379491, 5229092, 70805740, 944106760, 12426068215, 161793730426, 2087922762430, 26745380615078

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 5.

Column k=3 of A380235.

Cf. A348802, A348803, A348805, A348806, A348807, A348808, A348809, A348810, A348811.

A348805 a(n) = number of non-orientable genus 4 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 47, 1372, 31007, 611322, 11017122, 186044902, 2992773591, 46378655568, 697928466684, 10257901689164, 147883893647230

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 5.

Column k=4 of A380235.

Cf. A348802, A348803, A348804, A348806, A348807, A348808, A348809, A348810, A348811.

A348806 a(n) = number of non-orientable genus 5 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 473, 22556, 704066, 17691240, 387965547, 7743850792, 144265686318, 2549632137634, 43225637985830, 708619408979790

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 5.

Column k=5 of A380235.

Cf. A348802, A348803, A348804, A348805, A348807, A348808, A348809, A348810, A348811.

A348807 a(n) = number of non-orientable genus 6 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 7190, 469632, 18521632, 563764626, 14578260141, 336572753272, 7146006383642, 142229030736882, 2688967762932621

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 6.

Column k=6 of A380235.

Cf. A348802, A348803, A348804, A348805, A348806, A348808, A348809, A348810, A348811.

A348808 a(n) = number of non-orientable genus 7 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 144904, 11990766, 571333104, 20460879142, 611002852755, 16057491913346, 383591381459308, 8507419863898968

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 6.

Column k=7 of A380235.

Cf. A348802, A348803, A348804, A348805, A348806, A348807, A348809, A348810, A348811.

A348809 a(n) = number of non-orientable genus 8 maps with n edges.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 3534490, 352456980, 19724988666, 814875498464, 27678691047563, 817987730593078, 21764920947291140

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 6.

Column k=8 of A380235.

Cf. A348802, A348803, A348804, A348805, A348806, A348807, A348808, A348810, A348811.

cp's OEIS Frontend

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).

Views

Author

Keywords

Examples

Links

Crossrefs

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

A348802 a(n) = number of non-orientable genus 1 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348803 a(n) = number of non-orientable genus 2 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348804 a(n) = number of non-orientable genus 3 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348805 a(n) = number of non-orientable genus 4 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348806 a(n) = number of non-orientable genus 5 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348807 a(n) = number of non-orientable genus 6 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348808 a(n) = number of non-orientable genus 7 maps with n edges.

Views

Author

Keywords

Links

Crossrefs

A348809 a(n) = number of non-orientable genus 8 maps with n edges.

Views

Author

Keywords

Links

Crossrefs