A115605 - OEIS

%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