A190328 a(n) = n + [n*r/t] + [n*s/t]; r=1/2, s=sinh(Pi/2), t=cosh(Pi/2).

1, 3, 5, 7, 9, 12, 14, 16, 18, 20, 23, 25, 26, 28, 30, 33, 35, 37, 39, 41, 44, 46, 48, 50, 51, 54, 56, 58, 60, 62, 65, 67, 69, 71, 73, 76, 77, 79, 81, 83, 86, 88, 90, 92, 94, 97, 99, 101, 102, 104, 107, 109, 111, 113, 115, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 139, 141, 143, 145, 147, 150, 152, 153, 155, 157, 160

Offset

1,2

Comments

See A190326.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

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

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

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

Maple

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

Mathematica

r=1/2; s=Sinh[Pi/2]; t=Cosh[Pi/2];
f[n_] := n + Floor[n*s/r] + Floor[n*t/r];
g[n_] := n + Floor[n*r/s] + Floor[n*t/s];
h[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[f[n], {n, 1, 120}]  (* A190326 *)
Table[g[n], {n, 1, 120}]  (* A190327 *)
Table[h[n], {n, 1, 120}]  (* A190328 *)

Prog

(PARI) for(n=1, 100, print1(n + floor(n/(2*cosh(Pi/2))) + floor(n*tanh(Pi/2)), ", ")) \\ G. C. Greubel, Apr 04 2018
(Magma) R:=RealField(); [n + Floor(n/(2*Cosh(Pi(R)/2))) + Floor(n*Tanh(Pi(R)/2)): n in [1..100]]; // G. C. Greubel, Apr 04 2018

Crossrefs

Cf. A190326, A190327.

Sequence in context: A038663 A291154 A246405 * A248106 A033036 A198082

Adjacent sequences: A190325 A190326 A190327 * A190329 A190330 A190331

Keyword

nonn

Author

Clark Kimberling, May 08 2011

Status

approved