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 A105371 Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4). 7

%I

%S 1,1,1,0,-3,-8,-13,-13,0,34,89,144,144,0,-377,-987,-1597,-1597,0,4181,

%T 10946,17711,17711,0,-46368,-121393,-196418,-196418,0,514229,1346269,

%U 2178309,2178309,0,-5702887,-14930352,-24157817,-24157817,0,63245986,165580141

%N Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4).

%C Binomial transform of A105367.

%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-4,2,-1)

%F G.f. : (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4); a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4); (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*pi*n/5))

%F a(5n)=-F(-5n-1), a(5n+1)=a(5n+2)=-F(-5n-2), a(5n+3)=0, a(5n+4)=F(-5n-4). - Michael Somos Apr 9 2005

%o (PARI) a(n)=local(m); m=n%5+1; [1,-1,-1,0,1][m]*fibonacci(-n-(m<3)) /* Michael Somos Apr 9 2005 */

%Y Cf. A000045.

%K easy,sign

%O 0,5

%A _Paul Barry_, Apr 01 2005

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Last modified May 23 17:52 EDT 2013. Contains 225611 sequences.