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

%I A132677 #37 Mar 14 2025 17:49:27
%S A132677 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 A132677 -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 A132677 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 A132677 Period 3: repeat [1, 2, -3].
%C A132677 a(n) is proportional to its 6n-th differences.
%C A132677 Nonsimple continued fraction expansion of 1+sqrt(2/5) = 1.63245553... (see A010494). - _R. J. Mathar_, Mar 08 2012
%H A132677 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1).
%F A132677 G.f.: (1+3*x)/(1+x+x^2). - _Jaume Oliver Lafont_, Mar 24 2009
%F A132677 a(n) = cos(2*Pi*n/3) + 5*sin(2*Pi*n/3)/sqrt(3). - _R. J. Mathar_, Oct 08 2011
%F A132677 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 A132677 seq(op([1, 2, -3]), n=0..50); # _Wesley Ivan Hurt_, Jul 01 2016
%p A132677 A132677 := proc(n)
%p A132677     op(1+modp(n,3),[1,2,-3]) ;
%p A132677 end proc: # _R. J. Mathar_, Mar 14 2025
%t A132677 PadRight[{}, 100, {1, 2, -3}] (* _Wesley Ivan Hurt_, Jul 01 2016 *)
%o A132677 (PARI) a(n)=[1,2,-3][1+n%3] \\ _Jaume Oliver Lafont_, Mar 24 2009
%o A132677 (Magma) &cat [[1, 2, -3]^^30]; // _Wesley Ivan Hurt_, Jul 01 2016
%Y A132677 Cf. A000748, A010494, A049347, A101544.
%K A132677 sign,easy
%O A132677 0,2
%A A132677 _Paul Curtz_, Nov 15 2007