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A194163 a(n) = [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(3).

%I A194163 #13 Oct 29 2017 21:24:12
%S A194163 0,1,1,2,2,3,3,4,4,5,5,6,6,6,7,8,9,9,10,10,11,11,12,12,12,12,13,14,14,
%T A194163 15,16,16,16,17,18,18,18,19,19,20,20,21,21,21,22,23,23,23,24,25,25,25,
%U A194163 26,27,27,28,29,29,29,30,31,31,31,32,33,33,33,34,34,35,36,36
%N A194163 a(n) = [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(3).
%H A194163 G. C. Greubel, <a href="/A194163/b194163.txt">Table of n, a(n) for n = 1..5000</a>
%t A194163 r = Sqrt[3];
%t A194163 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194163 Table[a[n], {n, 1, 90}]      (* A194163 *)
%t A194163 s[n_] := Sum[a[k], {k, 1, n}]
%t A194163 Table[s[n], {n, 1, 100}]     (* A194164 *)
%o A194163 (PARI) for(n=1,50, print1(floor(sum(k=1,n, frac(k*sqrt(3)))), ", ")) \\ _G. C. Greubel_, Oct 29 2017
%Y A194163 Cf. A194164.
%K A194163 nonn
%O A194163 1,4
%A A194163 _Clark Kimberling_, Aug 18 2011