%I #11 Oct 08 2016 16:58:32
%S 1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,
%T 1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,
%U 1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1
%N [nr+kr]-[nr]-[kr], where r=1/sqrt(2), k=2, [ ]=floor.
%C See A187950. For k=1 instead of 2, see A080764 for which the position sequences of 0 and 1 are A001952 and A001951, respectively.
%H Chai Wah Wu, <a href="/A188374/b188374.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n)=[nr+2r]-[nr]-[2r], where r=1/sqrt(2).
%t r=2^(-1/2); k=2;
%t t=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r], {n,1,220}] (* A188374 *)
%t Flatten[Position[t,0] ] (* A188375 *)
%t Flatten[Position[t,1] ] (* A188376 *)
%o (Python)
%o from __future__ import division
%o from gmpy2 import isqrt
%o def A188374(n):
%o return int(isqrt((n+2)**2//2)-isqrt(n**2//2)) - 1 # _Chai Wah Wu_, Oct 08 2016
%Y Cf. A187950, A188375, A188376, A080764.
%K nonn
%O 1
%A _Clark Kimberling_, Mar 29 2011