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A105385 Expansion of (1-x^2)/(1-x^5). 1

%I

%S 1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,

%T 0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,

%U -1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1

%N Expansion of (1-x^2)/(1-x^5).

%C Binomial transform is A103311(n+1). Consecutive pair sums of A105384. Periodic {1,0,-1,0,0}.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1).

%F G.f.: (1+x)/(1 + x + x^2 + x^3 + x^4);

%F a(n) = sqrt(1/5 - 2*sqrt(5)/25)*cos(4*Pi*n/5 + Pi/10) + sqrt(5)*sin(4*Pi*n/5 + Pi/10)/5 + sqrt(2*sqrt(5)/25 + 1/5)*cos(2*Pi*n/5 + 3*Pi/10) + sqrt(5)*sin(2*Pi*n/5 + 3*Pi/10)/5.

%F a(n) = -(1/5)*((n mod 5) + ((n+2) mod 5) - ((n+3) mod 5) - ((n+4) mod 5)), with n >= 0. - _Paolo P. Lava_, Jun 01 2007

%F a(n) = A092202(n+1). - _R. J. Mathar_, Aug 28 2008

%F a(n) = a(n-1) - a(n-2) - a(n-3) - a(n-4); a(0)=1, a(1)=0, a(2)=-1, a(3)=0. - _Harvey P. Dale_, Mar 10 2013

%t CoefficientList[Series[(1-x^2)/(1-x^5),{x,0,100}],x] (* or *) PadRight[{},100,{1,0,-1,0,0}] (* or *) LinearRecurrence[{-1,-1,-1,-1},{1,0,-1,0},100] (* _Harvey P. Dale_, Mar 10 2013 *)

%Y Cf. A198517 (unsigned version).

%K sign,easy

%O 0,1

%A _Paul Barry_, Apr 02 2005

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Last modified April 3 21:54 EDT 2020. Contains 333207 sequences. (Running on oeis4.)