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A060783
Number of conics which pass through 3 points and are bitangent to a general curve of order n.
1
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, 880740, 981684, 1091056
OFFSET
0,3
LINKS
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.
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
E.g.f.: exp(x)*x^2*(4 + 8*x + x^2)/2. - Stefano Spezia, Jul 13 2024
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: A318150 A275133 A374387 * A296948 A125756 A173961
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