|
%I #19 Sep 26 2015 18:29:48
%S 0,0,2,7,31,128,549,2315,9826,41594,176242,746496,3162334,13395658,
%T 56745250,240376201,1018250793,4313378176,18271765435,77400436781,
%U 327873517634,1388894499108,5883451527348,24922700587008
%N Expansion of -x^2*(2 + x - 2*x^2 - x^3 + 2*x^4) / ( (x-1)*(1+x)*(1 + x + x^2)*(x^2 - x + 1)*(x^2 + 4*x - 1)*(x^2 - x - 1) ).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1,0,1,-3,-6,3,1).
%F Lim_{n->infinity} a(n+1)/a(n) = phi^3 = A098317.
%F a(n) = -A000035(n+1)/6 +A061347(n+2)/12 +A001076(n+1)/10 +3*A039834(n+1)/20 -A087204(n)/12. - _R. J. Mathar_, Dec 16 2011
%p A000035 := proc(n)
%p n mod 2 ;
%p end proc:
%p A061347 := proc(n)
%p op((n mod 3)+1,[-2,1,1]) ;
%p end proc:
%p A001076 := proc(n)
%p option remember;
%p if n <=1 then
%p n;
%p else
%p 4*procname(n-1)+procname(n-2) ;
%p end if;
%p end proc:
%p A039834 := proc(n)
%p (-1)^(n+1)*combinat[fibonacci](n) ;
%p end proc:
%p A087204 := proc(n)
%p op((n mod 6)+1,[2,1,-1,-2,-1,1]) ;
%p end proc:
%p A115605 := proc(n)
%p -A000035(n+1)/6 +A061347(n+2)/12 + A001076(n+1)/10 +3*A039834(n+1)/20 -A087204(n)/12 ;
%p end proc: # _R. J. Mathar_, Dec 16 2011
%t LinearRecurrence[{3,6,-3,-1,0,1,-3,-6,3,1},{0,0,2,7,31,128,549,2315,9826,41594},30] (* _Harvey P. Dale_, Dec 16 2011 *)
%o (PARI) concat([0,0],Vec((2+x-2*x^2-x^3+2*x^4)/((1-x)*(1+x)*(1+x+x^2)*(x^2-x+1)*(x^2+4*x-1)*(x^2-x-1))+O(x^99))) \\ _Charles R Greathouse IV_, Sep 27 2012
%Y Cf. A000045, A079962.
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_, Mar 13 2006
|
