A190055 a(n) = n + [n*r/t] + [n*s/t]; r=2, s=sin(Pi/3), t=csc(Pi/3).

2, 6, 10, 13, 16, 20, 24, 27, 30, 34, 38, 41, 44, 48, 51, 55, 58, 62, 65, 69, 72, 76, 79, 83, 86, 90, 93, 97, 100, 103, 107, 111, 114, 117, 121, 125, 128, 131, 135, 139, 142, 145, 149, 153, 155, 159, 163, 167, 169, 173, 177, 181, 183, 187, 191, 194, 197, 201, 205, 208, 211, 215, 219, 222, 225, 229, 233, 236, 239, 243, 246, 250, 253, 257, 260

Offset

1,1

Comments

See A190053.

Links

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

Formula

A190053: a(n) = n + [(n/2)*sin(Pi/3)] + [(n/2)*csc(Pi/3)].

A190054: b(n) = n + [2*n*csc(Pi/3)] + [n*(csc(Pi/3))^2].

A190055: c(n) = n + [2*n*sin(Pi/3)] + [n*(sin(Pi/3))^2].

Mathematica

r=2; s=Sin[Pi/3]; t=Csc[Pi/3];
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}]  (* A190053 *)
Table[b[n], {n, 1, 120}]  (* A190054 *)
Table[c[n], {n, 1, 120}]  (* A190055 *)

Prog

(PARI) for(n=1, 30, print1(n + floor(2*n*sin(Pi/3)) + floor(n*(sin(Pi/3))^2), ", ")) \\ G. C. Greubel, Jan 10 2018
(Magma) C<i> := ComplexField(); [n + Floor(2*n*Sin(Pi(C)/3)) + Floor(n*(Sin(Pi(C)/3))^2): n in [1..30]]; // G. C. Greubel, Jan 10 2018

Crossrefs

Cf. A190053, A190054.

Sequence in context: A066679 A086123 A144031 * A184929 A180123 A247785

Adjacent sequences: A190052 A190053 A190054 * A190056 A190057 A190058

Keyword

nonn

Author

Clark Kimberling, May 04 2011

Status

approved