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