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%I A194167 #5 Mar 30 2012 18:57:40
%S A194167 0,0,0,1,1,2,3,4,4,4,4,5,5,6,7,8,8,8,8,8,9,9,10,11,12,12,12,12,13,13,
%T A194167 14,15,16,16,16,16,16,17,18,18,19,20,20,20,21,21,22,22,23,24,24,24,24,
%U A194167 25,25,26,27,27,28,29,29,29,29,30,31,31,32,32,33,33,33,34,34,35
%N A194167 [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=(3+sqrt(5))/2, the golden ratio.
%t A194167 r = 1/2 + GoldenRatio;
%t A194167 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194167 Table[a[n], {n, 1, 90}]   (* A194167 *)
%t A194167 s[n_] := Sum[a[k], {k, 1, n}]
%t A194167 Table[s[n], {n, 1, 100}]  (* A194168 *)
%Y A194167 Cf. A194168.
%K A194167 nonn
%O A194167 1,6
%A A194167 _Clark Kimberling_, Aug 18 2011

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