

A030653


n^3*a(n) is 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 FultonKleimanMacPherson (pp. 156196 of Lect. Notes Math. n.997).


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

a(n)=n^3+3*n^2+3*n3.
G.f.: x*(4+7*x8*x^2+3*x^3)/(1x)^4. [Colin Barker, Sep 03 2012]


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*n3: n in [1..45]]; // Vincenzo Librandi, Jun 30 2011


CROSSREFS

Sequence in context: A106684 A239624 A179628 * 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



