OFFSET
1,1
COMMENTS
See A189932.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
Equals (n + floor(n*(csc(pi/5))^2) + floor(n*(cot(pi/5))^2))/2, for n>=1. - G. C. Greubel, Jan 13 2018
MATHEMATICA
r=1; s=Sin[Pi/5]^2; t=Cos[Pi/5]^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}] (*A005408*)
Table[b[n], {n, 1, 120}] (*A189932*)
Table[c[n], {n, 1, 120}] (*A189933*)
Table[b[n]/2, {n, 1, 120}] (*A189934*)
Table[c[n]/2, {n, 1, 120}] (*A189935*)
PROG
(PARI) for(n=1, 100, print1((n + floor(n/(sin(Pi/5))^2) + floor(n/(tan(Pi/5))^2))/2, ", ")) \\ G. C. Greubel, Jan 13 2018
(Magma) C<i> := ComplexField(); [(n + Floor(n/(Sin(Pi(C)/5))^2) + Floor(n/(Tan(Pi(C)/5))^2))/2: n in [1..100]]; // G. C. Greubel, Jan 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 01 2011
STATUS
approved