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A189480 [4rn]-4[rn], where r=sqrt(5) and [ ]=floor.

%I A189480 #15 Nov 18 2013 11:03:54
%S A189480 0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,
%T A189480 1,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,
%U A189480 1,2,3,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,2,3,0,1,2,3,0
%N A189480 [4rn]-4[rn], where r=sqrt(5) and [ ]=floor.
%C A189480 Suppose, in general, that a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b.  The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b.  These b+1 (or b) position sequences comprise a partition of the positive integers.
%H A189480 Ivan Panchenko, <a href="/A189480/b189480.txt">Table of n, a(n) for n = 1..1000</a>
%t A189480 r=Sqrt[5];
%t A189480 f[n_]:=Floor[4 n*r]-4*Floor[n*r];
%t A189480 t=Table[f[n],{n,1,320}] (*A189480*)
%t A189480 Flatten[Position[t,0]]  (*A190813*)
%t A189480 Flatten[Position[t,1]]  (*A190883*)
%t A189480 Flatten[Position[t,2]]  (*A190884*)
%t A189480 Flatten[Position[t,3]]  (*A190885*)
%Y A189480 Cf. A190813, A190883, A190884, A190885.
%K A189480 nonn
%O A189480 1,3
%A A189480 _Clark Kimberling_, Apr 23 2011