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A190008 a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sin(Pi/3), t=csc(Pi/3).

%I A190008 #18 Sep 08 2022 08:45:56
%S A190008 1,4,7,10,12,15,18,20,22,25,28,31,33,36,38,41,43,46,49,52,54,57,59,62,
%T A190008 64,67,70,73,75,77,80,83,85,88,91,94,96,98,101,104,106,109,112,115,
%U A190008 116,119,122,125,127,130,133,136,137,140,143,146,148,151,154,156,158,161,164,167,169,172,175,177,179,182,185,188,190
%N A190008 a(n) = n + [n*r/t] + [n*s/t];  r=1, s=sin(Pi/3), t=csc(Pi/3).
%C A190008 See A190006.
%H A190008 G. C. Greubel, <a href="/A190008/b190008.txt">Table of n, a(n) for n = 1..10000</a>
%F A190008 A190006:  a(n) = n + [n*sin(Pi/3)] + [n*csc(Pi/3)].
%F A190008 A190007:  b(n) = n + [n*csc(Pi/3)] + [n*(csc(Pi/3))^2].
%F A190008 A190008:  c(n) = n + [n*sin(Pi/3)] + [n*(sin(Pi/3))^2].
%t A190008 r=1; s=Sin[Pi/3]; t=Csc[Pi/3];
%t A190008 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A190008 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A190008 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A190008 Table[a[n], {n, 1, 120}]  (* A190006 *)
%t A190008 Table[b[n], {n, 1, 120}]  (* A190007 *)
%t A190008 Table[c[n], {n, 1, 120}]  (* A190008 *)
%o A190008 (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 A190008 Cf. A190006, A190007.
%K A190008 nonn
%O A190008 1,2
%A A190008 _Clark Kimberling_, May 03 2011