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 A030653 n^3*a(n) is the number of circles in complex projective plane tangent to three smooth curves of degree n in general position. 1
 4, 23, 60, 121, 212, 339, 508, 725, 996, 1327, 1724, 2193, 2740, 3371, 4092, 4909, 5828, 6855, 7996, 9257, 10644, 12163, 13820, 15621, 17572, 19679, 21948, 24385, 26996, 29787, 32764, 35933, 39300, 42871, 46652, 50649, 54868, 59315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES See formula for enumeration of contacts in Fulton-Kleiman-MacPherson (pp. 156-196 of Lect. Notes Math. n.997). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 William Fulton, Steven Kleiman, Robert MacPherson, About the enumeration of contacts, Algebraic Geometry — Open Problems, Lecture Notes in Mathematics, 1983 vol. 997. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = n^3 + 3*n^2 + 3*n - 3. G.f.: x*(4 + 7*x - 8*x^2 + 3*x^3)/(1-x)^4. - Colin Barker, Sep 03 2012 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Oct 20 2022 MATHEMATICA LinearRecurrence[{4, -6, 4, -1}, {4, 23, 60, 121}, 40] (* Harvey P. Dale, Nov 29 2014 *) PROG (Magma) [n^3+3*n^2+3*n-3: n in [1..45]]; // Vincenzo Librandi, Jun 30 2011 (PARI) a(n)=n^3 + 3*n^2 + 3*n - 3 \\ Charles R Greathouse IV, Feb 10 2017 CROSSREFS Sequence in context: A239624 A179628 A339392 * A085505 A065972 A132112 Adjacent sequences: A030650 A030651 A030652 * A030654 A030655 A030656 KEYWORD nonn,nice,easy AUTHOR Paolo Dominici (pl.dm(AT)libero.it) STATUS approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)