A190004 A190002/2.

2, 4, 7, 9, 11, 14, 16, 19, 21, 23, 26, 28, 30, 33, 35, 38, 40, 42, 45, 47, 50, 52, 54, 57, 59, 61, 64, 66, 69, 71, 73, 76, 78, 80, 83, 85, 88, 90, 92, 95, 97, 100, 102, 104, 107, 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

Offset: 1

Author

Clark Kimberling, May 03 2011

Keywords

• nonn

Comments

See A180002.

First differs from A182761 at n=55: a(55)=130, A182761(55)=131. - Bruno Berselli, Jun 04 2013

Links

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

Crossrefs

Cf. A190002, A190003.

Programs

Magma

[(n + Floor(n*(Sinh(1))^2) + Floor(n*(Cosh(1))^2))/2: n in [1..100]]; // G. C. Greubel, Jan 11 2018

Mathematica

r=1; s=Sinh[1]^2; t=Cosh[1]^2;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 120}]  (* A190002 *)
Table[b[n], {n, 1, 120}]  (* A190003 *)
Table[c[n], {n, 1, 120}]  (* A005408 *)
Table[a[n]/2, {n, 1, 120}](* A190004 *)
Table[b[n]/2, {n, 1, 120}](* A182760 *)

PARI

for(n=1,100, print1((n + floor(n*(sinh(1))^2) + floor(n*(cosh(1))^2))/2, ", ")) \\ G. C. Greubel, Jan 11 2018

Formula

A190002: a(n) = n + [n*(sinh(1))^2] + [n*(cosh(1))^2].

A190003: b(n) = n + [n*(csch(1))^2] + [n*(coth(1))^2].

A190004: a(n)/2 = (n + [n*(sinh(1))^2] + [n*(cosh(1))^2])/2.

A005408: c(n) = 2*n - 1.