%I #27 Mar 19 2022 00:22:47
%S 8,497,9352,81473,451976,1863793,6230792,17817857,45159688,103980401,
%T 221416328,441884737,834981512,1505831153,2608352776,4361946113,
%U 7072141832,11155800817,17171487368,25855681601
%N n^4*a(n) is the number of spheres in complex projective space tangent to 4 smooth surfaces of degree n in general position.
%D See formula for enumeration of contacts in Fulton-Kleiman-MacPherson (pp. 156-196 of Lect. Notes Math. n.997).
%H Vincenzo Librandi, <a href="/A030654/b030654.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F a(n) = n^8 + 4*n^6 - 2*n^4 + 4*n^2 + 1.
%F 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
%F 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
%p 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
%t 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 *)
%o (Magma) [n^8+4*n^6-2*n^4+4*n^2+1: n in [1..30]]; // _Vincenzo Librandi_, May 31 2011
%o (PARI) a(n)=n^8 + 4*n^6 - 2*n^4 + 4*n^2 + 1 \\ _Charles R Greathouse IV_, Feb 10 2017
%K nonn,nice,easy
%O 1,1
%A Paolo Dominici (pl.dm(AT)libero.it)