A171113 - OEIS

%I #28 Jun 15 2021 14:46:02

%S 0,0,15,675,7915,41310,145383,404185,959115,2029980,3939295,7139823,

%T 12245355,20064730,31639095,48282405,71625163,103661400,146798895,

%U 203912635,278401515,374248278,496082695,649247985,839870475,1074932500,1362348543,1711044615

%N a(n) is the Severi degree for curves of degree n and cogenus 3.

%H Harvey P. Dale, <a href="/A171113/b171113.txt">Table of n, a(n) for n = 1..1000</a>

%H Florian Block, <a href="https://arxiv.org/abs/1006.0218">Computing node polynomials for plane curves</a>, arXiv:1006.0218 [math.AG], 2010-2011; Math. Res. Lett. 18, (2011), no. 4, 621-643.

%H Florian Block, Susan Jane Colley, and Gary Kennedy, <a href="https://arxiv.org/abs/1303.5308">Computing Severi degrees with long-edge graphs</a>, Bulletin of the Brazilian Mathematical Society, New Series 45.4 (2014): 625-647. Also arXiv:1303.5308 [math.AG], 2013 (see first page).

%H P. Di Francesco and C. Itzykson, <a href="https://doi.org/10.1007/978-1-4612-4264-2_4">Quantum Intersection Rings</a>, in: The Moduli Space of Curves, Birkhäuser Boston, 1995; on <a href="https://arxiv.org/abs/hep-th/9412175">arXiv</a>, arXiv:hep-th/9412175, 1994. See Proposition 2 (iii) and the following Remark (a).

%H Sergey Fomin and Grigory Mikhalkin, <a href="https://doi.org/10.4171/JEMS/238">Labeled floor diagrams for plane curves</a>, Journal of the European Mathematical Society 012.6 (2010): 1453-1496; arXiv:<a href="https://arxiv.org/abs/0906.3828">0906.3828</a> [math.AG], 2009-2010.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,15,675,7915,41310,145383,404185,959115},30] (* _Harvey P. Dale_, Jun 15 2021 *)

%o (Python)

%o [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

%Y Cf. A171108, A328551, A328552.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Sep 27 2010

%E Terms a(7) and beyond from _Andrey Zabolotskiy_, Jan 12 2021