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a(n) = [2^n/(1 - cos(1/n))] - [2^n/(-1 + cot(1/n))] - [2^n/(1 - cos(1/n)) - 2^n/(-1 + cot(1/n))], where [ ] = floor.
5

%I #11 Dec 20 2024 03:56:30

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

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

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

%N a(n) = [2^n/(1 - cos(1/n))] - [2^n/(-1 + cot(1/n))] - [2^n/(1 - cos(1/n)) - 2^n/(-1 + cot(1/n))], where [ ] = floor.

%F a(n) = [2^n/(1 - cos(1/n))] - [2^n/(-1 + cot(1/n))] - [2^n/(1 - cos(1/n)) - 2^n/(-1 + cot(1/n))], where [ ] = floor.

%t z = 50; u = Table[Floor[2^n/(1 - Cos[1/n])], {n, 1, z}] (* A332430 *)

%t v = Table[Floor[2^n/(-1 + Cot[1/n])], {n, 1, z}] (* A332431 *)

%t u - v (* A332432 *)

%t w = Table[Floor[2^n/(1 - Cos[1/n]) - 2^n/(-1 + Cot[1/n])], {n, 1, z}]

%t u - v - w (* A332479 *)

%Y Cf. A333186, A333189, A332430, A332431, A332432, A332433.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 05 2020