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%I #11 Sep 08 2022 08:45:56
%S 1,3,6,8,10,12,15,17,18,21,23,26,27,30,32,34,36,38,41,43,45,47,49,52,
%T 53,56,58,61,62,64,67,69,71,73,76,78,80,82,84,87,88,91,93,96,97,99,
%U 102,104,106,108,111,113,114,117,119,122,123,126,128,130,132,134,137,139,141,143,146,148,149,152,154,157,158,161,163,165,167
%N a(n) = n + [n*r/t] + [n*s/t]; r=1/2, s=sin(Pi/3), t=csc(Pi/3).
%C See A190056.
%H G. C. Greubel, <a href="/A190058/b190058.txt">Table of n, a(n) for n = 1..10000</a>
%F A190056: a(n) = n + [2*n*sin(Pi/3)] + [2*n*csc(Pi/3)].
%F A190057: b(n) = n + [(n/2)*csc(Pi/3)] + [n*(csc(Pi/3))^2].
%F A190058: c(n) = n + [(n/2)*sin(Pi/3)] + [n*(sin(Pi/3))^2].
%t r=1/2; s=Sin[Pi/3]; t=Csc[Pi/3];
%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t Table[a[n], {n, 1, 120}] (* A190056 *)
%t Table[b[n], {n, 1, 120}] (* A190057 *)
%t Table[c[n], {n, 1, 120}] (* A190058 *)
%o (PARI) for(n=1,30, print1(n + floor(n*sin(Pi/3)/2) + floor(n*(sin(Pi/3))^2), ", ")) \\ _G. C. Greubel_, Jan 10 2018
%o (Magma) C<i> := ComplexField(); [n + Floor(n*Sin(Pi(C)/3)/2) + Floor(n*(Sin(Pi(C)/3))^2): n in [1..30]]; // _G. C. Greubel_, Jan 10 2018
%Y Cf. A190056, A190057.
%K nonn
%O 1,2
%A _Clark Kimberling_, May 04 2011
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