A131722 - OEIS

%I #24 Dec 12 2023 09:16:20

%S 0,10,10,10,10,10,0,10,10,10,10,10,0,10,10,10,10,10,0,10,10,10,10,10,

%T 0,10,10,10,10,10,0,10,10,10,10,10,0,10,10,10,10,10,0,10,10,10,10,10,

%U 0,10,10,10,10,10,0,10,10,10,10,10,0,10,10,10,10,10,0,10

%N Period 6: repeat [0, 10, 10, 10, 10, 10].

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F a(n) = 10 * sign(n mod 6). - _Wesley Ivan Hurt_, Mar 21 2014

%F From _Wesley Ivan Hurt_, Jun 21 2016: (Start)

%F G.f.: 10*x*(1+x+x^2+x^3+x^4)/(1-x^6).

%F a(n) = a(n-6) for n>5.

%F a(n) = 10 * sin(n*Pi/6)^2 * (9 + 8*cos(n*Pi/3) + 2*cos(2*n*Pi/3))/3. (End)

%p A131722:=n->10*signum(n mod 6); seq(A131722(n), n=0..100); # _Wesley Ivan Hurt_, Mar 21 2014

%t Table[10 Sign[Mod[n, 6]], {n, 0, 100}] (* _Wesley Ivan Hurt_, Mar 21 2014 *)

%t PadRight[{},120,{0,10,10,10,10,10}] (* _Harvey P. Dale_, Jan 10 2023 *)

%o (Magma) &cat [[0, 10, 10, 10, 10, 10]^^20]; // _Wesley Ivan Hurt_, Jun 21 2016

%K nonn,easy,less

%O 0,2

%A _Paul Curtz_, Sep 15 2007