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A170946
Number of sensed unrooted combinatorial maps with n edges.
12
1, 2, 5, 20, 107, 870, 9436, 122840, 1863359, 32019826, 613981447, 12989756316, 300559406027, 7550660328494, 204687564072918, 5955893472990664, 185158932576089787, 6125200100394894738, 214837724735760642773, 7963817561236130021156, 311101285883236139915989
OFFSET
0,2
COMMENTS
Also number of "dessins d'enfants" with n edges. - Mark van Hoeij, Jan 23 2011
a(n) also counts the Feynman diagrams of the QED vacuum polarization with 2*n vertices: fermion lines (resp. boson lines, vertices) of the Feynman diagrams correspond to the vertices (resp. edges, darts) of the combinatorial maps, and the circular order of the edges around each vertex in a map is encoded in the topology of the corresponding Feynman diagram. - Andrey Zabolotskiy, Jan 28 2025
LINKS
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.
CROSSREFS
Row sums of A379438 and A380615.
Cf. A170947 (achiral), A214816 (unsensed).
Cf. A268558 (inv. Euler Transf.)
Sequence in context: A227096 A152562 A006867 * A296727 A201224 A305922
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 21 2010
EXTENSIONS
a(0)=1 prepended by Andrew Howroyd, Jan 28 2025
STATUS
approved