A132951 - OEIS

%I #34 Feb 26 2024 13:41:33

%S 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 -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 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 Period 6: repeat [1, 3, 1, -1, -3, -1].

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1).

%F a(n) = 3*a(n-1)-a(n-3)+3*a(n-4).

%F 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 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 a(n) = a(n-6) = A131531(n+3)+A131531(n+1)+3*A131531(n+2). - _R. J. Mathar_, Apr 04 2008

%F a(n) = A109007(n+2) * A130151(n). - _Wesley Ivan Hurt_, Jun 22 2013

%t PadRight[{},120,{1,3,1,-1,-3,-1}] (* _Harvey P. Dale_, Feb 26 2024 *)

%o (PARI) a(n)=[1,3,1,-1,-3,-1][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011

%o (Magma) &cat [[1, 3, 1, -1, -3, -1]: n in [0..20]]; // _Wesley Ivan Hurt_, Nov 18 2022

%Y Cf. A109007, A130151, A131531.

%K sign,easy,less

%O 0,2

%A _Paul Curtz_, Nov 22 2007

%E Edited by _N. J. A. Sloane_, May 16 2008 at the suggestion of _R. J. Mathar_.