A380234 -id:A380234 - 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.

A006443 Number of achiral planar maps with n edges.

Original entry on oeis.org

1, 2, 4, 14, 47, 184, 761, 3314, 14997, 69886, 333884, 1626998, 8067786, 40580084, 206734083, 1064666724, 5536480877, 29036188788, 153450351924, 816503772830, 4371551433888

Offset: 0

N. J. A. Sloane

An achiral map is a map with a sense-reversing automorphism.

The planar maps considered are connected and may contain loops and parallel edges. - Andrew Howroyd, Jan 13 2025

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
Timothy R. Walsh, Number of sensed planar maps with n edges and m vertices, p. 43.
Nicholas C. Wormald, Counting unrooted planar maps, Discrete Math. 36 (1981), no. 2, 205-225.

Column k=0 of A380234.

Cf. A006384 (sensed), A006385 (unsensed), A006444 (2-connected), A006445 (3-connected).

a(n) = 2*A006385(n) - A006384(n). [Liskovets eq 3a] - R. J. Mathar, Oct 01 2011

a(0)=1 prepended by Andrew Howroyd, Jan 13 2025

a(20) added by Andrew Howroyd, Jan 20 2025

A170947 Number of achiral combinatorial maps with n edges.

Original entry on oeis.org

2, 5, 20, 85, 418, 2242, 12828, 77777, 493286, 3260485, 22314484, 157735801, 1147285362, 8570960234, 65611620808, 513963377327, 4113363020482, 33598074760393, 279764563749076, 2372822051513583, 20481425601917742, 179795508212739402, 1604084463778300348, 14536376462636666141

Offset: 1

N. J. A. Sloane, Feb 21 2010

nonn

Achiral maps are also called reflexible.

Antonio Breda d'Azevedo, Alexander Mednykh, and Roman Nedela, Table of n, a(n) for n = 1..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.

Row sums of A380234.

Cf. A170946 (sensed), A170948 (chiral pairs), A214816 (unsensed).

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).

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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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A006443 Number of achiral planar maps with n edges.

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A170947 Number of achiral combinatorial maps with n edges.

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