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A060784 Number of double tangents of order n. 1
0, 4, 0, 0, 28, 120, 324, 700, 1320, 2268, 3640, 5544, 8100, 11440, 15708, 21060, 27664, 35700, 45360, 56848, 70380, 86184, 104500, 125580, 149688, 177100, 208104, 243000, 282100, 325728, 374220, 427924, 487200, 552420, 623968 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

H. Brocard and T. Lemoyne: Courbes géométriques remarquables (courbes spéciales) Planes et Gauches. Tome I, Paris: Albert Blanchard, 1967 [First publ. 1919]; see p. 375.

C.G.J. Jacobi, (Bericht ueber die zur Bekanntmachung geeigneten), Verhandlungen der Koenigl. Preuss. Akademie der Wiss. Berlin, 1850, p. 209, Jun 13, 1850. [Wolfdieter Lang, Oct 09 2001]

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

D. Ayala and R. Cavalieri, Counting bitangents with stable maps, arXiv:math/0505139 [math.AG], 2005.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = n*(n-2)*(n-3)*(n+3)/2.

From Colin Barker, Mar 16 2020: (Start)

G.f.: 4*x*(1 - 5*x + 10*x^2 - 3*x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

PROG

(PARI) a(n)={n*(n - 2)*(n - 3)*(n + 3)/2} \\ Harry J. Smith, Jul 11 2009

(PARI) concat(0, Vec(4*x*(1 - 5*x + 10*x^2 - 3*x^3) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Mar 16 2020

CROSSREFS

Sequence in context: A232357 A196302 A307186 * A181204 A191417 A307050

Adjacent sequences:  A060781 A060782 A060783 * A060785 A060786 A060787

KEYWORD

nonn,easy

AUTHOR

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 28 2001

STATUS

approved

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Last modified June 2 11:20 EDT 2020. Contains 334771 sequences. (Running on oeis4.)