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a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sqrt(5/3), t=sqrt(3/5).
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%I #10 Sep 08 2022 08:45:57

%S 3,7,11,15,19,23,27,31,35,38,43,47,50,55,59,62,66,71,74,78,83,86,90,

%T 94,98,102,106,110,114,118,122,126,130,133,138,142,145,150,154,157,

%U 161,166,169,173,178,181,185,189,193,197,201,205,209,213,217,221,225,228,233,237,240,245,249,252,256,261,264,268,273,276,280,284,288

%N a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sqrt(5/3), t=sqrt(3/5).

%C See A190347.

%H G. C. Greubel, <a href="/A190349/b190349.txt">Table of n, a(n) for n = 1..10000</a>

%F A190347: f(n) = n + [n*sqrt(5/3)] + [n*sqrt(3/5)].

%F A190348: g(n) = n + [n*sqrt(3/5)] + [3*n/5].

%F A190349: h(n) = 2*n + [n*sqrt(5/3)] + [n/3].

%t r=1; s=(5/3)^(1/2); t=1/s;

%t f[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t g[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t h[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[f[n], {n, 1, 120}] (* A190347 *)

%t Table[g[n], {n, 1, 120}] (* A190348 *)

%t Table[h[n], {n, 1, 120}] (* A190349 *)

%o (PARI) for(n=1,100, print1(2*n + floor(n*sqrt(5/3)) + floor(n/3), ", ")) \\ _G. C. Greubel_, Apr 05 2018

%o (Magma) [2*n + Floor(n*Sqrt(5/3)) + Floor(n/3): n in [1..100]]; // _G. C. Greubel_, Apr 05 2018

%Y Cf. A190347, A190348.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 09 2011