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A190007 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sin(Pi/3), t=csc(Pi/3).

%I A190007 #14 Oct 20 2024 01:42:16
%S A190007 3,6,10,13,16,20,24,27,31,34,37,41,45,48,52,55,58,62,65,69,73,76,79,
%T A190007 83,86,90,94,97,100,104,107,110,115,118,121,125,128,131,136,139,142,
%U A190007 146,149,152,156,160,163,167,170,173,177,181,184,188,191,194,198,201,205,209,212,215,219,222,226,230,233,236,240,243,246,251,254
%N A190007 a(n) = n + [n*r/s] + [n*t/s];  r=1, s=sin(Pi/3), t=csc(Pi/3).
%C A190007 See A190006.
%H A190007 G. C. Greubel, <a href="/A190007/b190007.txt">Table of n, a(n) for n = 1..10000</a>
%F A190007 A190006:  a(n) = n + [n*sin(Pi/3)] + [n*csc(Pi/3)].
%F A190007 A190007:  b(n) = n + [n*csc(Pi/3)] + [n*(csc(Pi/3))^2].
%F A190007 A190008:  c(n) = n + [n*sin(Pi/3)] + [n*(sin(Pi/3))^2].
%t A190007 r=1; s=Sin[Pi/3]; t=Csc[Pi/3];
%t A190007 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A190007 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A190007 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A190007 Table[a[n], {n, 1, 120}]  (* A190006 *)
%t A190007 Table[b[n], {n, 1, 120}]  (* A190007 *)
%t A190007 Table[c[n], {n, 1, 120}]  (* A190008 *)
%o A190007 (PARI) for(n=1,100, print1(n + floor(n/sin(Pi/3)) + floor(n/(sin(Pi/3))^2), ", ")) \\ _G. C. Greubel_, Jan 11 2018
%o A190007 (Magma) C<i> := ComplexField(); [n + Floor(n/Sin(Pi(C)/3)) + Floor(n/(Sin(Pi(C)/3))^2): n in [1..100]]; // _G. C. Greubel_, Jan 11 2018
%Y A190007 Cf. A190006, A190008.
%K A190007 nonn,easy
%O A190007 1,1
%A A190007 _Clark Kimberling_, May 03 2011