A158459 - OEIS

%I #55 Dec 12 2023 08:04:48

%S 0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,

%T 2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,

%U 0,3,2,1,0,3,2,1,0,3,2,1,0,3,2,1,0,3,2

%N Period 4: repeat [0, 3, 2, 1].

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).

%F G.f.: x*(x^2+2*x+3)/(1-x^4).

%F a(n) = A102370(n) (mod 4).

%F a(n) = 3/2-(-1)^n/2+sin(n*Pi/2)-cos(n*Pi/2). - _Richard Choulet_, Apr 07 2009

%F a(n) = -n (mod 4). - _M. F. Hasler_, Jan 13 2012; formula simplified by _Arkadiusz Wesolowski_, Jul 03 2012

%F a(n) = (3-(-1)^n-2*I^(n*(n+1)))/2. - _Bruno Berselli_, Jul 03 2012

%F a(n) = floor(107/3333*10^(n+1)) mod 10. - _Hieronymus Fischer_, Jan 04 2013

%F a(n) = floor(19/85*4^(n+1)) mod 4. - _Hieronymus Fischer_, Jan 04 2013

%F a(n) = ((n+1) mod 4)+(-1)^((n+1) mod 4). - _Wesley Ivan Hurt_, May 18 2014

%F a(n) = 3*n mod 4. - _Gary Detlefs_, May 24 2014

%F a(n) = a(n-4) for n>3. - _Wesley Ivan Hurt_, Jul 09 2016

%p seq(op([0, 3, 2, 1]), n=0..50); # _Wesley Ivan Hurt_, Jul 09 2016

%t Flatten@Table[{0, 3, 2, 1}, {22}] (* _Arkadiusz Wesolowski_, Jul 03 2012 *)

%o (PARI) A158459(n)=(-n)%4 \\ _M. F. Hasler_, Jan 13 2012

%o (Haskell)

%o a158459 = (`mod` 4) . negate

%o a158459_list = cycle [0,3,2,1]  -- _Reinhard Zumkeller_, Feb 22 2013

%o (Magma) &cat [[0, 3, 2, 1]^^30]; // _Wesley Ivan Hurt_, Jul 09 2016

%Y Cf. A010873, A102370.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Mar 19 2009

%E Better definition from _M. F. Hasler_, Jan 13 2012