A060783 Number of conics which pass through 3 points and are bitangent to a general curve of order n.

0, 0, 4, 36, 132, 340, 720, 1344, 2296, 3672, 5580, 8140, 11484, 15756, 21112, 27720, 35760, 45424, 56916, 70452, 86260, 104580, 125664, 149776, 177192, 208200, 243100, 282204, 325836, 374332, 428040, 487320, 552544, 624096, 702372, 787780

Offset

0,3

Links

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

H. Brocard and T. Lemoyne, Courbes géométriques remarquables (courbes spéciales) Planes et Gauches, Tome I, Paris: Albert Blanchard, 1967 [First publ. 1919]; see p. 411.

J. Steiner, Aufgaben und Lehrsätze, Journal für die reine und angewandte Mathematik, Zeitschriftenband (1855), Vol. 49, p. 273.

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

Formula

a(n) = (n-1)*n*(n^2 + 3*n - 6)/2.

G.f.: 4*x^2*(1+4*x-2*x^2)/(1-x)^5. [Colin Barker, Mar 26 2012]

Mathematica

Table[(n-1)n (n^2+3n-6)/2, {n, 0, 40}] (* Harvey P. Dale, Apr 05 2020 *)

Prog

(PARI) { for (n=0, 1000, write("b060783.txt", n, " ", (n-1)*n*(n^2 + 3*n - 6)/2); ) } \\ Harry J. Smith, Jul 11 2009

Crossrefs

Sequence in context: A045490 A318150 A275133 * A296948 A125756 A173961

Adjacent sequences: A060780 A060781 A060782 * A060784 A060785 A060786

Keyword

nonn,easy

Author

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

Extensions

More terms from Jason Earls, Apr 29 2001

Status

approved