A171113 a(n) is the Severi degree for curves of degree n and cogenus 3.
0, 0, 15, 675, 7915, 41310, 145383, 404185, 959115, 2029980, 3939295, 7139823, 12245355, 20064730, 31639095, 48282405, 71625163, 103661400, 146798895, 203912635, 278401515, 374248278, 496082695, 649247985, 839870475, 1074932500, 1362348543, 1711044615
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Florian Block, Computing node polynomials for plane curves, arXiv:1006.0218 [math.AG], 2010-2011; Math. Res. Lett. 18, (2011), no. 4, 621-643.
- Florian Block, Susan Jane Colley, and Gary Kennedy, Computing Severi degrees with long-edge graphs, Bulletin of the Brazilian Mathematical Society, New Series 45.4 (2014): 625-647. Also arXiv:1303.5308 [math.AG], 2013 (see first page).
- P. Di Francesco and C. Itzykson, Quantum Intersection Rings, in: The Moduli Space of Curves, Birkhäuser Boston, 1995; on arXiv, arXiv:hep-th/9412175, 1994. See Proposition 2 (iii) and the following Remark (a).
- Sergey Fomin and Grigory Mikhalkin, Labeled floor diagrams for plane curves, Journal of the European Mathematical Society 012.6 (2010): 1453-1496; arXiv:0906.3828 [math.AG], 2009-2010.
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Mathematica
LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,15,675,7915,41310,145383,404185,959115},30] (* Harvey P. Dale, Jun 15 2021 *) -
Python
[0, 0] + [(9*d**6 + 9*d**4 + 423*d**3 - 829*d)//2 - 27*d**5 - 229*d**2 + 525 for d in range(3, 30)] # Andrey Zabolotskiy, Jan 12 2021
Formula
a(n) = 9*n^6/2 - 27*n^5 + 9*n^4/2 + 423*n^3/2 - 229*n^2 - 829*n/2 + 525 for n > 2. - Andrey Zabolotskiy, Jan 19 2021
Extensions
Terms a(7) and beyond from Andrey Zabolotskiy, Jan 12 2021