A170946
Number of sensed unrooted combinatorial maps with n edges.
Original entry on oeis.org
1, 2, 5, 20, 107, 870, 9436, 122840, 1863359, 32019826, 613981447, 12989756316, 300559406027, 7550660328494, 204687564072918, 5955893472990664, 185158932576089787, 6125200100394894738, 214837724735760642773, 7963817561236130021156, 311101285883236139915989
Offset: 0
- Andrew Howroyd, Table of n, a(n) for n = 0..400 (terms 1..30 from Antonio Breda d'Azevedo, Alexander Mednykh and Roman Nedela)
- 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.
- N. M. Adrianov, N. Ya. Amburg, V. A. Dremov, Yu. A. Levitskaya, E. M. Kreines, Yu. Yu. Kochetkov, V. F. Nasretdinova and G. B. Shabat, Catalog of dessins d'enfants with <= 4 edges, arXiv:0710.2658 [math.AG], 2007.
- R. J. Mathar, Feynman diagrams of the QED vacuum polarization, vixra:1901.0148 (2019), Section V. Computed up to a(5), plotted up to a(4).
- R. de Mello Koch and S. Ramgoolam, Strings from Feynman graph counting: without large N, Phys Rev D, 85 (2012) 026007; arXiv:1110.4858 [hep-th], 2011-2012. The terms in Eq. (D.10) from a(7) on are erroneous.
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.
Original entry on oeis.org
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
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;
...
A380618
Number of sensed combinatorial maps with n edges and 2 vertices.
Original entry on oeis.org
1, 2, 8, 38, 275, 2614, 30346, 415360, 6513999, 115063118, 2259975228, 48860184539, 1153140907207, 29502289676802, 813371784160602, 24040797257734161, 758379326971459945, 25432414455826532993, 903508909333199982128, 33897272145242834426910, 1339265974992611047296679
Offset: 1
-
\\ Needs G(), InvEulerMTS from A380615.
seq(n, k=2)={my(y='y); Vec(polcoef(InvEulerMTS(G(n, y*(1 + O(y^k)))), k, y))}
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
-
\\ Needs G(), InvEulerMTS from A380615.
seq(n, k=3)={my(y='y); Vec(polcoef(InvEulerMTS(G(n, y*(1 + O(y^k)))), k, y))}
A380617
Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
Original entry on oeis.org
1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 16, 28, 26, 12, 3, 53, 121, 128, 82, 28, 6, 206, 528, 686, 505, 239, 68, 10, 817, 2516, 3638, 3192, 1802, 686, 157, 20, 3620, 12302, 20250, 19976, 13268, 6078, 1876, 372, 35, 16361, 63643, 114669, 126876, 95422, 50954, 19346, 5100, 845, 70
Offset: 0
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 | 16, 28, 26, 12, 3;
5 | 53, 121, 128, 82, 28, 6;
6 | 206, 528, 686, 505, 239, 68, 10;
7 | 817, 2516, 3638, 3192, 1802, 686, 157, 20;
8 | 3620, 12302, 20250, 19976, 13268, 6078, 1876, 372, 35;
...
Showing 1-5 of 5 results.
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