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 A132677 Period 3: repeat [1, 2, -3]. 2

%I

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

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

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

%N Period 3: repeat [1, 2, -3].

%C a(n) is proportional to its 6n-th differences.

%C Nonsimple continued fraction expansion of 1+sqrt(2/5) = 1.63245553.. (see A010494) - _R. J. Mathar_, Mar 08 2012

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

%F a(n) = (1/3)*{-4*(n mod 3)+5*[(n+1) mod 3]-[(n+2) mod 3]}. - _Paolo P. Lava_, Nov 30 2007

%F G.f.: (1+3*x)/(1+x+x^2). - _Jaume Oliver Lafont_, Mar 24 2009

%F a(n) = cos(2*Pi*n/3)+5*sin(2*Pi*n/3)/sqrt(3). - _R. J. Mathar_, Oct 08 2011

%F a(n) + a(n-1) + a(n-2) = 0 for n>1, a(n) = a(n-3) for n>2. - _Wesley Ivan Hurt_, Jul 01 2016

%p seq(op([1, 2, -3]), n=0..50); # _Wesley Ivan Hurt_, Jul 01 2016

%t PadRight[{}, 100, {1, 2, -3}] (* _Wesley Ivan Hurt_, Jul 01 2016 *)

%o (PARI) a(n)=[1,2,-3][1+n%3] \\ _Jaume Oliver Lafont_, Mar 24 2009

%o (MAGMA) &cat [[1, 2, -3]^^30]; // _Wesley Ivan Hurt_, Jul 01 2016

%Y Cf. A000748, A010494, A049347, A101544.

%K sign,easy

%O 0,2

%A _Paul Curtz_, Nov 15 2007

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)