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a(n) = n + [n*r/s] + [n*t/s]; r=1/2, s=sinh(Pi/2), t=cosh(Pi/2).
4

%I #13 Sep 08 2022 08:45:57

%S 2,4,6,8,11,13,15,17,19,22,24,27,29,32,34,36,38,40,43,45,47,49,52,55,

%T 57,59,61,64,66,68,70,72,75,78,80,82,85,87,89,91,93,96,98,100,103,105,

%U 108,110,112,114,117,119,121,123,125,129,131,133,135,138,140,142,144,146,149,151,154,156,158,161,163,165,167,170

%N a(n) = n + [n*r/s] + [n*t/s]; r=1/2, s=sinh(Pi/2), t=cosh(Pi/2).

%C See A190326.

%H G. C. Greubel, <a href="/A190327/b190327.txt">Table of n, a(n) for n = 1..10000</a>

%F A190326: f(n) = n + [2*n*sinh(Pi/2)] + [2*n*cosh(Pi/2)].

%F A190327: g(n) = n + [n*csch(Pi/2)/2] + [n*coth(Pi/2)].

%F A190328: h(n) = n + [n*sech(Pi/2)/2] + [n*tanh(Pi/2)].

%p r:=1/2: s:=sinh(Pi/2): t:=cosh(Pi/2): seq(n+floor(n*r/s)+floor(n*t/s),n=1..80); # _Muniru A Asiru_, Apr 05 2018

%t r=1/2; s=Sinh[Pi/2]; t=Cosh[Pi/2];

%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}] (* A190326 *)

%t Table[g[n], {n, 1, 120}] (* A190327 *)

%t Table[h[n], {n, 1, 120}] (* A190328 *)

%o (PARI) for(n=1,100, print1(n + floor(n/(2*sinh(Pi/2))) + floor(n/tanh(Pi/2)), ", ")) \\ _G. C. Greubel_, Apr 04 2018

%o (Magma) R:=RealField(); [n + Floor(n/(2*Sinh(Pi(R)/2))) + Floor(n/Tanh(Pi(R)/2)): n in [1..100]]; // _G. C. Greubel_, Apr 04 2018

%Y Cf. A190326, A190328.

%K nonn

%O 1,1

%A _Clark Kimberling_, May 08 2011