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A190004 A190002/2.

%I A190004 #12 Sep 08 2022 08:45:56
%S A190004 2,4,7,9,11,14,16,19,21,23,26,28,30,33,35,38,40,42,45,47,50,52,54,57,
%T A190004 59,61,64,66,69,71,73,76,78,80,83,85,88,90,92,95,97,100,102,104,107,
%U A190004 109,111,114,116,119,121,123,126,128,130,133,135,138,140,142,145,147,150,152,154,157,159,161,164,166,169,171,173,176
%N A190004 A190002/2.
%C A190004 See A180002.
%C A190004 First differs from A182761 at n=55: a(55)=130, A182761(55)=131. - _Bruno Berselli_, Jun 04 2013
%H A190004 G. C. Greubel, <a href="/A190004/b190004.txt">Table of n, a(n) for n = 1..10000</a>
%F A190004 A190002:  a(n) = n + [n*(sinh(1))^2] + [n*(cosh(1))^2].
%F A190004 A190003:  b(n) = n + [n*(csch(1))^2] + [n*(coth(1))^2].
%F A190004 A190004:  a(n)/2 = (n + [n*(sinh(1))^2] + [n*(cosh(1))^2])/2.
%F A190004 A005408:  c(n) = 2*n - 1.
%t A190004 r=1; s=Sinh[1]^2; t=Cosh[1]^2;
%t A190004 a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
%t A190004 b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
%t A190004 c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
%t A190004 Table[a[n], {n, 1, 120}]  (* A190002 *)
%t A190004 Table[b[n], {n, 1, 120}]  (* A190003 *)
%t A190004 Table[c[n], {n, 1, 120}]  (* A005408 *)
%t A190004 Table[a[n]/2, {n, 1, 120}](* A190004 *)
%t A190004 Table[b[n]/2, {n, 1, 120}](* A182760 *)
%o A190004 (PARI) for(n=1,100, print1((n + floor(n*(sinh(1))^2) + floor(n*(cosh(1))^2))/2, ", ")) \\ _G. C. Greubel_, Jan 11 2018
%o A190004 (Magma) [(n + Floor(n*(Sinh(1))^2) + Floor(n*(Cosh(1))^2))/2: n in [1..100]]; // _G. C. Greubel_, Jan 11 2018
%Y A190004 Cf. A190002, A190003.
%K A190004 nonn
%O A190004 1,1
%A A190004 _Clark Kimberling_, May 03 2011