A380621 -id:A380621 - cp's OEIS frontend

A380616 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.

1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 17, 33, 30, 13, 3, 79, 198, 208, 118, 35, 6, 554, 1571, 1894, 1232, 472, 104, 12, 5283, 16431, 21440, 15545, 6879, 1914, 315, 27, 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65, 966156, 3288821, 4799336, 4019360, 2163112, 787065, 196267, 32857, 3407, 175

Offset: 0

Andrew Howroyd, Jan 28 2025

By duality, also the number of unsensed combinatorial maps with n edges and k faces.

			Triangle begins:
n\k |     1       2       3       4       5      6     7     8   9
----+--------------------------------------------------------------
  0 |     1;
  1 |     1,      1;
  2 |     2,      2,      1;
  3 |     5,      8,      5,      2;
  4 |    17,     33,     30,     13,      3;
  5 |    79,    198,    208,    118,     35,     6;
  6 |   554,   1571,   1894,   1232,    472,   104,   12;
  7 |  5283,  16431,  21440,  15545,   6879,  1914,  315,   27;
  8 | 65346, 213831, 296952, 233027, 115134, 37311, 7881, 1021, 65;
  ...

Row sums are A214816.
Main diagonal is A006082(n+1).
Columns 1..3 are A054499, A380620, A380621.
Cf. A053979 (rooted), A277741 (planar), A380615 (sensed), A380617 (achiral).

T(n,k) = (A380615(n,k) + A380617(n,k))/2.

A380619 Number of sensed combinatorial maps with n edges and 3 vertices.

Original entry on oeis.org

1, 5, 34, 288, 3102, 39242, 573654, 9484003, 175036065, 3568736050, 79697415569, 1935425955944, 50794210191337, 1432898704970561, 43244525933606928, 1390448844972918928, 47455314531812444788, 1713525997666221196906, 65266335503957271588042, 2615307907226341637828915

Offset: 2

Andrew Howroyd, Jan 28 2025

nonn

By duality, also the number of sensed combinatorial maps with n edges and 3 faces.

Andrew Howroyd, Table of n, a(n) for n = 2..200

Column 3 of A380615.

Cf. A380618 (2 vertices), A380621 (unsensed).

\\ Needs G(), InvEulerMTS from A380615.
seq(n, k=3)={my(y='y); Vec(polcoef(InvEulerMTS(G(n, y*(1 + O(y^k)))), k, y))}

A380620 Number of unsensed combinatorial maps with n edges and 2 vertices.

Original entry on oeis.org

1, 2, 8, 33, 198, 1571, 16431, 213831, 3288821

Offset: 1

Andrew Howroyd, Jan 28 2025

By duality, also the number of unsensed combinatorial maps with n edges and 2 faces.

Column 2 of A380616.

Cf. A380239 (planar), A380618 (sensed), A380621 (3 vertices).

cp's OEIS Frontend

A380616 Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.

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A380619 Number of sensed combinatorial maps with n edges and 3 vertices.

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A380620 Number of unsensed combinatorial maps with n edges and 2 vertices.

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