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A190003 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=(sinh(1))^2, t=(cosh(1))^2.

%I A190003 #18 Sep 08 2022 08:45:56
%S A190003 2,6,10,12,16,20,24,26,30,34,36,40,44,48,50,54,58,62,64,68,72,74,78,
%T A190003 82,86,88,92,96,98,102,106,110,112,116,120,124,126,130,134,136,140,
%U A190003 144,148,150,154,158,162,164,168,172,174,178,182,186,188,192,196,198,202,206,210,212,216,220,224,226,230,234,236,240
%N A190003 a(n) = n + [n*r/s] + [n*t/s]; r=1, s=(sinh(1))^2, t=(cosh(1))^2.
%C A190003 See A190002.
%H A190003 G. C. Greubel, <a href="/A190003/b190003.txt">Table of n, a(n) for n = 1..10000</a>
%F A190003 A190002:  a(n) = n + [n*(sinh(1))^2] + [n*(cosh(1))^2].
%F A190003 A190003:  b(n) = n + [n*(csch(1))^2] + [n*(coth(1))^2].
%F A190003 A005408:  c(n) = 2*n - 1.
%p A190003 seq(n+floor(n/s)+floor(n*t/s), n=1..100); # _Robert Israel_, Jan 12 2018
%t A190003 r=1; s=Sinh[1]^2; t=Cosh[1]^2;
%t A190003 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A190003 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A190003 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A190003 Table[a[n], {n, 1, 120}]  (* A190002 *)
%t A190003 Table[b[n], {n, 1, 120}]  (* A190003 *)
%t A190003 Table[c[n], {n, 1, 120}]  (* A005408 *)
%t A190003 Table[a[n]/2, {n, 1, 120}](* A190004 *)
%t A190003 Table[b[n]/2, {n, 1, 120}](* A182760 *)
%o A190003 (PARI) for(n=1,100, print1(n + floor(n/(sinh(1))^2) + floor(n/(tanh(1))^2), ", ")) \\ _G. C. Greubel_, Jan 11 2018
%o A190003 (Magma) [n + Floor(n/(Sinh(1))^2) + Floor(n/(Tanh(1))^2): n in [1..100]]; // _G. C. Greubel_, Jan 11 2018
%Y A190003 Cf. A190002, A182760.
%K A190003 nonn
%O A190003 1,1
%A A190003 _Clark Kimberling_, May 03 2011