A190369 - OEIS

A190369

a(n) = n + [n*r/s] + [n*t/s] + [n*u/s]; r=sin(Pi/5), s=cos(Pi/5), t=sin(2*Pi/5), u=cos(2*Pi/5).

2, 5, 9, 11, 14, 19, 22, 25, 28, 31, 34, 38, 41, 45, 47, 51, 54, 58, 61, 64, 68, 70, 74, 78, 81, 83, 87, 90, 95, 97, 100, 104, 106, 109, 114, 117, 120, 123, 126, 131, 133, 137, 140, 142, 146, 150, 153, 156, 159, 163, 166, 169, 173, 176, 179, 182, 186, 190, 192, 195, 199, 202, 206, 209, 212, 215, 218, 221, 226, 228, 232, 235, 238, 241

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A190368.

LINKS

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

FORMULA

A190368: f(n) = n + floor(n*cot(Pi/5)) + floor(2*n*cos(Pi/5)) + floor(n*cos(2*Pi/5)/sin(Pi/5)).

A190369: g(n) = n + floor(n*tan(Pi/5)) + floor(2*n*sin(Pi/5)) + floor(n*cos(2*Pi/5)/cos(Pi/5)).

A190370: h(n) = n + floor(n*sec(Pi/5)/2) + floor(n*csc(Pi/5)/2) + floor(n*cot(2*Pi/5)).

A190371: i(n) = n + floor(n*sin(Pi/5)/cos(2*Pi/5)) + floor(n*cos(Pi/5)/cos(2*Pi/5)) + floor(n*tan(2*Pi/5)).

MAPLE

r:=sin(Pi/5): s:=cos(Pi/5): t:=sin(2*Pi/5): u:=cos(2*Pi/5): seq(n+floor(n*r/s)+floor(n*t/s)+floor(n*u/s), n=1..80); # Muniru A Asiru, Apr 08 2018

MATHEMATICA

r=Sin[Pi/5]; s=Cos[Pi/5]; t=Sin[2*Pi/5]; u=Cos[2*Pi/5];

f[n_] := n + Floor[n*s/r] + Floor[n*t/r] + Floor[n*u/r];

g[n_] := n + Floor[n*r/s] + Floor[n*t/s] + Floor[n*u/s];

h[n_] := n + Floor[n*r/t] + Floor[n*s/t] + Floor[n*u/t];

i[n_] := n + Floor[n*r/u] + Floor[n*s/u] + Floor[n*t/u];

Table[f[n], {n, 1, 120}] (* A190368 *)

Table[g[n], {n, 1, 120}] (* A190369 *)

Table[h[n], {n, 1, 120}] (* A190370 *)

Table[i[n], {n, 1, 120}] (* A190371 *)

PROG

(PARI) for(n=1, 100, print1(n + floor(n*tan(Pi/5)) + floor(2*n*sin(Pi/5)) + floor(n*cos(2*Pi/5)/cos(Pi/5)), ", ")) \\ G. C. Greubel, Apr 05 2018

(Magma) R:=RealField(); [n + Floor(n*Tan(Pi(R)/5)) + Floor(2*n*Sin(Pi(R)/5)) + Floor(n*Cos(2*Pi(R)/5)/Cos(Pi(R)/5)): n in [1..100]]; // G. C. Greubel, Apr 05 2018

CROSSREFS

Cf. A190368, A190370, A190371.

Sequence in context: A020907 A206904 A189472 * A067568 A190329 A329791

Adjacent sequences: A190366 A190367 A190368 * A190370 A190371 A190372

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 09 2011

STATUS

approved