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A190007 a(n) = n + [n*r/s] + [n*t/s];  r=1, s=sin(pi/3), t=csc(pi/3). 3
3, 6, 10, 13, 16, 20, 24, 27, 31, 34, 37, 41, 45, 48, 52, 55, 58, 62, 65, 69, 73, 76, 79, 83, 86, 90, 94, 97, 100, 104, 107, 110, 115, 118, 121, 125, 128, 131, 136, 139, 142, 146, 149, 152, 156, 160, 163, 167, 170, 173, 177, 181, 184, 188, 191, 194, 198, 201, 205, 209, 212, 215, 219, 222, 226, 230, 233, 236, 240, 243, 246, 251, 254 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A190006.

LINKS

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

FORMULA

A190006:  a(n) = n + [n*sin(pi/3)] + [n*csc(pi/3].

A190007:  b(n) = n + [n*csc(pi/3)] + [n*(csc(pi/3))^2].

A190008:  c(n) = n + [n*sin(pi/3)] + [n*(sin(pi/3))^2].

MATHEMATICA

r=1; 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}]  (*A190006*)

Table[b[n], {n, 1, 120}]  (*A190007*)

Table[c[n], {n, 1, 120}]  (*A190008*)

PROG

(PARI) for(n=1, 100, print1(n + floor(n/sin(Pi/3)) + floor(n/(sin(Pi/3))^2), ", ")) \\ G. C. Greubel, Jan 11 2018

(MAGMA) C<i> := ComplexField(); [n + Floor(n/Sin(Pi(C)/3)) + Floor(n/(Sin(Pi(C)/3))^2): n in [1..100]]; // G. C. Greubel, Jan 11 2018

CROSSREFS

Cf. A190006, A190008.

Sequence in context: A310051 A080667 A277722 * A310052 A310053 A001952

Adjacent sequences:  A190004 A190005 A190006 * A190008 A190009 A190010

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 03 2011

STATUS

approved

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Last modified August 20 02:06 EDT 2019. Contains 326136 sequences. (Running on oeis4.)