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%I #15 Sep 08 2022 08:45:56
%S 2,6,10,13,16,20,24,27,30,34,38,41,44,48,51,55,58,62,65,69,72,76,79,
%T 83,86,90,93,97,100,103,107,111,114,117,121,125,128,131,135,139,142,
%U 145,149,153,155,159,163,167,169,173,177,181,183,187,191,194,197,201,205,208,211,215,219,222,225,229,233,236,239,243,246,250,253,257,260
%N a(n) = n + [n*r/t] + [n*s/t]; r=2, s=sin(Pi/3), t=csc(Pi/3).
%C See A190053.
%H G. C. Greubel, <a href="/A190055/b190055.txt">Table of n, a(n) for n = 1..10000</a>
%F A190053: a(n) = n + [(n/2)*sin(Pi/3)] + [(n/2)*csc(Pi/3)].
%F A190054: b(n) = n + [2*n*csc(Pi/3)] + [n*(csc(Pi/3))^2].
%F A190055: c(n) = n + [2*n*sin(Pi/3)] + [n*(sin(Pi/3))^2].
%t r=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}] (* A190053 *)
%t Table[b[n], {n, 1, 120}] (* A190054 *)
%t Table[c[n], {n, 1, 120}] (* A190055 *)
%o (PARI) for(n=1,30, print1(n + floor(2*n*sin(Pi/3)) + floor(n*(sin(Pi/3))^2), ", ")) \\ _G. C. Greubel_, Jan 10 2018
%o (Magma) C<i> := ComplexField(); [n + Floor(2*n*Sin(Pi(C)/3)) + Floor(n*(Sin(Pi(C)/3))^2): n in [1..30]]; // _G. C. Greubel_, Jan 10 2018
%Y Cf. A190053, A190054.
%K nonn
%O 1,1
%A _Clark Kimberling_, May 04 2011
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