OFFSET
1,4
COMMENTS
All terms are divisible by 9: (a(n)) = 9*(42, 10003, 325759, 3746706, 24967791, ...). Satisfies a linear recurrence with characteristic polynomial (x-1)^11. - M. F. Hasler, Oct 30 2019
LINKS
Colin Barker, 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.
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.
Israel Vainsencher, Enumeration of n-fold tangent hyperplanes to a surface, arXiv preprint alg-geom/9312012, 1993-1994; J. Algebraic Geom., 4 (1995), 503-526. See Section 5.1.2.
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = (81/40)*n^10 - (81/4)*n^9 - (27/8)*n^8 + (2349/4)*n^7 - (1044)*n^6 - (127071/20)*n^5 + (128859/8)*n^4 + (59097/2)*n^3 - (3528381/40)*n^2 - (946929/20)*n + 153513 for n > 3.
G.f.: 9*x^4*(42 + 9541*x + 218036*x^2 + 706592*x^3 + 34135*x^4 - 290191*x^5 + 181478*x^6 - 45302*x^7 + 677*x^8 + 1664*x^9 - 192*x^10)/(1 - x)^11. - M. F. Hasler, Oct 30 2019
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>9. - Colin Barker, Oct 30 2019
PROG
(PARI) {A328552(n, c=[9961, 305795, 2799396, 11895551, 28175817, 40446774, 36208620, 19852560, 6123600, 816480], p=9)=if(n<4, 0, sum(k=1, min(#c, n-=4), c[k]*p*=(n-k+1)/k, 378))} \\ M. F. Hasler, Oct 30 2019
(PARI) concat([0, 0, 0], Vec(9*x^4*(42 + 9541*x + 218036*x^2 + 706592*x^3 + 34135*x^4 - 290191*x^5 + 181478*x^6 - 45302*x^7 + 677*x^8 + 1664*x^9 - 192*x^10) / (1 - x)^11 + O(x^40))) \\ Colin Barker, Oct 30 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 29 2019
EXTENSIONS
New name and a(1)=a(2)=a(3)=0 from Andrey Zabolotskiy, Jan 19 2021
STATUS
approved