A030654 n^4*a(n) is the number of spheres in complex projective space tangent to 4 smooth surfaces of degree n in general position.

8, 497, 9352, 81473, 451976, 1863793, 6230792, 17817857, 45159688, 103980401, 221416328, 441884737, 834981512, 1505831153, 2608352776, 4361946113, 7072141832, 11155800817, 17171487368, 25855681601

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

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Formula

a(n) = n^8 + 4*n^6 - 2*n^4 + 4*n^2 + 1.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9); a(1)=8, a(2)=497, a(3)=9352, a(4)=81473, a(5)=451976, a(6)=1863793, a(7)=6230792, a(8)=17817857, a(9)=45159688. - Harvey P. Dale, Apr 10 2012

G.f.: x*(8 + 425*x + 5167*x^2 + 14525*x^3 + 14651*x^4 + 5083*x^5 + 461*x^6 - x^7 + x^8)/(1-x)^9. - Colin Barker, Apr 18 2012

Maple

A030654:=n->n^8 + 4*n^6 - 2*n^4 + 4*n^2 + 1; seq(A030654(n), n=1..30); # Wesley Ivan Hurt, Feb 08 2014

Mathematica

Table[n^8+4n^6-2n^4+4n^2+1, {n, 20}] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {8, 497, 9352, 81473, 451976, 1863793, 6230792, 17817857, 45159688}, 20] (* Harvey P. Dale, Apr 10 2012 *)

Prog

(Magma) [n^8+4*n^6-2*n^4+4*n^2+1: n in [1..30]]; // Vincenzo Librandi, May 31 2011
(PARI) a(n)=n^8 + 4*n^6 - 2*n^4 + 4*n^2 + 1 \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Sequence in context: A282180 A240398 A265231 * A281136 A228292 A082385

Adjacent sequences: A030651 A030652 A030653 * A030655 A030656 A030657

Keyword

nonn,nice,easy

Author

Paolo Dominici (pl.dm(AT)libero.it)

Status

approved