A188009 - OEIS

%I #23 Aug 30 2022 08:12:30

%S 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,

%T 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,

%U 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

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

%C See A188014.

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

%F a(n) = A123740(n-2), n >= 3. - _Wolfdieter Lang_, Jun 27 2011

%t r=(1+5^(1/2))/2; k=2;

%t t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}]   (* A188009 *)

%t Flatten[Position[t,0]]  (* A188010 *)

%t Flatten[Position[t,1]]  (* First column of array A101866 *)

%o (Python)

%o from math import isqrt

%o 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

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

%K nonn

%O 1

%A _Clark Kimberling_, Mar 19 2011