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A190054 a(n) = n + [n*r/s] + [n*t/s];  r=2, s=sin(Pi/3), t=csc(Pi/3). 3
4, 8, 13, 18, 22, 27, 32, 36, 41, 46, 50, 55, 60, 64, 69, 73, 78, 83, 87, 92, 97, 101, 106, 111, 115, 120, 125, 129, 133, 139, 143, 147, 153, 157, 161, 167, 171, 175, 181, 185, 189, 194, 199, 203, 208, 213, 217, 222, 227, 231, 236, 241, 245, 250, 255, 259, 264, 268, 273, 278, 282, 287, 292, 296, 301, 306, 310, 315, 320, 324, 328, 334 (list; graph; refs; listen; history; text; internal format)
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, A190055.

Sequence in context: A312099 A312100 A312101 * A312102 A312103 A312104

Adjacent sequences:  A190051 A190052 A190053 * A190055 A190056 A190057

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 04 2011

STATUS

approved

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Last modified August 20 14:50 EDT 2019. Contains 326152 sequences. (Running on oeis4.)