login
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.
1
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
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
KEYWORD
nonn,nice,easy
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it)
STATUS
approved