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a(n) = [n*u + n*v] - [n*u] - [n*v], where u=sin(2*Pi/5), v=cos(2*Pi/5), and []=floor.
3

%I #11 Sep 08 2022 08:45:57

%S 1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,

%T 1,0,0,0,0,0,1,1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,1,0,1,1,0,

%U 0,1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,1,1,1,1,1,1,0,1

%N a(n) = [n*u + n*v] - [n*u] - [n*v], where u=sin(2*Pi/5), v=cos(2*Pi/5), and []=floor.

%H G. C. Greubel, <a href="/A190230/b190230.txt">Table of n, a(n) for n = 1..10000</a>

%t u = Sin[2Pi/5]; v = Cos[2Pi/5];

%t f[n_] := Floor[n*u + n*v] - Floor[n*u] - Floor[n*v]

%t t = Table[f[n], {n, 1, 120}] (* A190230 *)

%t Flatten[Position[t, 0]] (* A190231 *)

%t Flatten[Position[t, 1]] (* A190232 *)

%o (PARI) for(n=1,30, print1(floor(n*(sin(Pi/5) + cos(Pi/5))) - floor(n*cos(Pi/5)) - floor(n*sin(Pi/5)), ", ")) \\ _G. C. Greubel_, Dec 27 2017

%o (Magma) C<i> := ComplexField(); [Floor(n*(Sin(Pi(C)/5) + Cos(Pi(C)/5))) - Floor(n*Sin(Pi(C)/5)) - Floor(n*Cos(Pi(C)/5)): n in [1..30]]; // _G. C. Greubel_, Dec 27 2017

%Y Cf. A190231, A190232, A190227.

%K nonn

%O 1

%A _Clark Kimberling_, May 06 2011