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A060783
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Number of conics which pass through 3 points and are bitangent to a general curve of order n.
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1
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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
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OFFSET
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0,3
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REFERENCES
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H. Brocard and T. Lemoyne: Courbes geometriques remarquables (courbes speciales) Planes et Gauches. Tome I, Paris: Albert Blanchard, 1967 [First publ. 1919]; see p. 411.
Steiner, Crelle's J., Vol. 49, p. 273.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
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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]
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PROG
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(PARI) { for (n=0, 1000, write("b060783.txt", n, " ", (n-1)*n*(n^2 + 3*n - 6)/2); ) } [From Harry J. Smith, Jul 11 2009]
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CROSSREFS
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Sequence in context: A144298 A072109 A045490 * A125756 A173961 A035287
Adjacent sequences: A060780 A060781 A060782 * A060784 A060785 A060786
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KEYWORD
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nonn,easy
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AUTHOR
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Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 28 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Apr 29 2001
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STATUS
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approved
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