cp's OEIS Frontend

A132951 Period 6: repeat [1, 3, 1, -1, -3, -1].

%I A132951 #34 Feb 26 2024 13:41:33
%S A132951 1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,
%T A132951 -3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,
%U A132951 3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1,1,3,1,-1,-3,-1
%N A132951 Period 6: repeat [1, 3, 1, -1, -3, -1].
%H A132951 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).
%F A132951 a(n) = 3*a(n-1)-a(n-3)+3*a(n-4).
%F A132951 O.g.f.: (1+3*x+x^2)/((x+1)*(x^2-x+1)) = -(1/3)/(x+1)+(1/3)*(4*x+4)/(x^2-x+1). - _R. J. Mathar_, Nov 28 2007
%F A132951 a(n) = -(1/3)*(-1)^n+(4/3)*cos(Pi*n/3)+(4*3^0.5/3)*sin(Pi*n/3). - _Richard Choulet_, Jan 02 2008
%F A132951 a(n) = a(n-6) = A131531(n+3)+A131531(n+1)+3*A131531(n+2). - _R. J. Mathar_, Apr 04 2008
%F A132951 a(n) = A109007(n+2) * A130151(n). - _Wesley Ivan Hurt_, Jun 22 2013
%t A132951 PadRight[{},120,{1,3,1,-1,-3,-1}] (* _Harvey P. Dale_, Feb 26 2024 *)
%o A132951 (PARI) a(n)=[1,3,1,-1,-3,-1][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011
%o A132951 (Magma) &cat [[1, 3, 1, -1, -3, -1]: n in [0..20]]; // _Wesley Ivan Hurt_, Nov 18 2022
%Y A132951 Cf. A109007, A130151, A131531.
%K A132951 sign,easy,less
%O A132951 0,2
%A A132951 _Paul Curtz_, Nov 22 2007
%E A132951 Edited by _N. J. A. Sloane_, May 16 2008 at the suggestion of _R. J. Mathar_.