A188009 a(n) = [nr] - [nr-kr] - [kr], where r=(1+sqrt(5))/2, k=2, [ ]=floor.

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1

Offset

1

Comments

See A188014.

Links

Table of n, a(n) for n=1..136.

Formula

a(n) = [nr] - [nr-2r] - [2r], where r=(1+sqrt(5))/2.

a(n) = A123740(n-2), n >= 3. - Wolfdieter Lang, Jun 27 2011

Mathematica

r=(1+5^(1/2))/2; k=2;
t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r], {n, 1, 220}]   (* A188009 *)
Flatten[Position[t, 0]]  (* A188010 *)
Flatten[Position[t, 1]]  (* First column of array A101866 *)

Prog

(Python)
from math import isqrt
def A188009(n): return (n+isqrt(m:=5*n**2)>>1)-(n-2+isqrt(m-20*(n-1))>>1)-3 if n > 1 else 0 # Chai Wah Wu, Aug 29 2022

Crossrefs

Cf. A001622, A188014, A188010, A101866, A187950, A123740.

Sequence in context: A188041 A261990 A144601 * A353812 A353813 A353814

Adjacent sequences: A188006 A188007 A188008 * A188010 A188011 A188012

Keyword

nonn

Author

Clark Kimberling, Mar 19 2011

Status

approved