A131806 - OEIS

%I #32 Mar 02 2024 01:26:48

%S 0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,

%T 4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,

%U 0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6,0,2,4,6

%N Period 4: repeat [0, 2, 4, 6].

%H Salvatore Gambino, <a href="http://digilander.libero.it/salgam">Terne pitagoriche primitive</a>

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

%F a(n) = 3+(-1)^n+2*(-1)^((2*n+1-(-1)^n)/4).

%F G.f.: 2*x^2*(1+2*x+3*x^2)/((1-x)*(1+x)*(1+x^2)). a(n) = 2*A010873(n-1). - _R. J. Mathar_, Jan 15 2008

%F From _Wesley Ivan Hurt_, Jul 09 2016: (Start)

%F a(n) = a(n-4) for n>4.

%F a(n) = 3 + cos(n*Pi) + 2*cos(n*Pi/2) - 2*sin(n*Pi/2) + I*sin(n*Pi). (End)

%p seq(op([0, 2, 4, 6]), n=1..40); # _Wesley Ivan Hurt_, Jul 09 2016

%t PadRight[{}, 100, {0, 2, 4, 6}] (* _Wesley Ivan Hurt_, Jul 09 2016 *)

%o (Magma) &cat [[0, 2, 4, 6]^^30]; // _Wesley Ivan Hurt_, Jul 09 2016

%Y Cf. A010873.

%K nonn,easy

%O 1,2

%A Salvatore Gambino (salvatore.gambino(AT)fastwebnet.it), Oct 04 2007

%E More terms from _R. J. Mathar_, Jan 15 2008