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A174737 a(n) = a(n-1) - a(n-2), with a(0)=2, a(1)=-1. 2

%I

%S 2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,

%T -2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,

%U -1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2,1,3,2,-1,-3,-2

%N a(n) = a(n-1) - a(n-2), with a(0)=2, a(1)=-1.

%D Rosen, Discrete Mathematics and its Applications, McGraw-Hill, 2007, p. 456, Question 1b.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1).

%F From _Paolo P. Lava_, Aug 25 2010: (Start)

%F a(n) = ((1/2)-(1/2)*i*sqrt(3))^n + ((1/2)+(1/2)*i*sqrt(3))^n + ((2/3)*i)*sqrt(3)*(((1/2)+(1/2)*i*sqrt(3))^n - ((1/2)-(1/2)*i*sqrt(3))^n), with n >= 0.

%F a(n) = (1/6)*((n mod 6) - 2*((n+1) mod 6) - 3*((n+2) mod 6) - ((n+3) mod 6) + 2*((n+4) mod 6) + 3*((n+5) mod 6)), with n >= 0. (End)

%F G.f.: ( 2-3*x ) / ( 1-x+x^2 ). - _R. J. Mathar_, Jan 08 2011

%p a[0] := 2: a[1] := -1: for n from 2 to 80 do a[n] := a[n-1]-a[n-2] end do: seq(a[n], n = 0 .. 75); # _Emeric Deutsch_, Apr 05 2010

%K easy,sign

%O 0,1

%A Zachary Berger (zsb1244(AT)rit.edu), Mar 28 2010

%E Typo in definition fixed by _Emeric Deutsch_, Apr 05 2010

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Last modified June 15 10:14 EDT 2021. Contains 345048 sequences. (Running on oeis4.)