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A171113 a(n) is the Severi degree for curves of degree n and cogenus 3. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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).

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

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 *)

PROG

(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

CROSSREFS

Cf. A171108, A328551, A328552.

Sequence in context: A349889 A279531 A079600 * A166186 A351182 A266519

Adjacent sequences:  A171110 A171111 A171112 * A171114 A171115 A171116

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 27 2010

EXTENSIONS

Terms a(7) and beyond from Andrey Zabolotskiy, Jan 12 2021

STATUS

approved

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Last modified June 30 02:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)