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A190549 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,1) and []=floor.

%I A190549 #11 Jul 04 2017 18:27:10
%S A190549 2,3,1,3,0,2,4,1,3,0,2,4,1,3,1,2,0,2,3,1,3,0,2,4,1,3,1,2,0,2,3,1,3,0,
%T A190549 2,4,1,3,1,2,4,2,3,1,2,0,2,3,1,3,0,2,4,1,3,1,2,0,2,3,1,3,0,2,4,1,3,1,
%U A190549 2,4,2,3,1,3,0,2,3,1,3,0,2,4,1,3,1,2,0,2,3,1,3,0,2,4,1,3,1,2,0,2,3,1,3,0,2,4,1,3,1,2,4,1,3,1,2,0,2,3,1,3,0,2,4,1,3,1,2,0,2,3,1,3,0,2,4,1,3
%N A190549 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,1) and []=floor.
%C A190549 Write 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 position sequences comprise a partition of the positive integers.
%C A190549 Examples:
%C A190549 (golden ratio,2,1):  A190427-A190430
%C A190549 (sqrt(2),2,0):  A190480-A190482
%C A190549 (sqrt(2),2,1):  A190483-A190486
%C A190549 (sqrt(2),3,0):  A190487-A190490
%C A190549 (sqrt(2),3,1):  A190491-A190495
%C A190549 (sqrt(2),3,2):  A190496-A190500
%C A190549 (sqrt(2),4,c):  A190544-A190566
%H A190549 G. C. Greubel, <a href="/A190549/b190549.txt">Table of n, a(n) for n = 1..1000</a>
%t A190549 r = Sqrt[2]; b = 4; c = 1;
%t A190549 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
%t A190549 t = Table[f[n], {n, 1, 200}] (* A190549 *)
%t A190549 Flatten[Position[t, 0]]          (* A190550 *)
%t A190549 Flatten[Position[t, 1]]          (* A190551 *)
%t A190549 Flatten[Position[t, 2]]          (* A190552 *)
%t A190549 Flatten[Position[t, 3]]          (* A190553 *)
%t A190549 Flatten[Position[t, 4]]          (* A190554 *)
%Y A190549 Cf. A190550, A190551, A190552, A190553.
%K A190549 nonn
%O A190549 1,1
%A A190549 _Clark Kimberling_, May 12 2011