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A194173 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(6).

%I A194173 #12 Nov 12 2017 03:03:08
%S A194173 0,1,1,2,2,3,3,4,4,4,5,6,6,7,7,8,8,8,9,10,10,11,12,12,13,13,13,14,14,
%T A194173 15,15,16,17,17,18,18,18,19,19,20,21,21,22,22,23,23,24,24,24,25,26,26,
%U A194173 27,27,28,28,29,29,29,30,30,31,32,32,33,33,33,34,34,34,35,36,37
%N A194173 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(6).
%H A194173 G. C. Greubel, <a href="/A194173/b194173.txt">Table of n, a(n) for n = 1..5000</a>
%t A194173 r = Sqrt[6];
%t A194173 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194173 Table[a[n], {n, 1, 90}]   (* A194173 *)
%t A194173 s[n_] := Sum[a[k], {k, 1, n}]
%t A194173 Table[s[n], {n, 1, 100}]  (* A194174 *)
%o A194173 (PARI) a(n) = floor(sum(k=1, n, frac(sqrt(6)*k))); \\ _Michel Marcus_, Nov 12 2017
%Y A194173 Cf. A194173.
%K A194173 nonn
%O A194173 1,4
%A A194173 _Clark Kimberling_, Aug 18 2011