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A194169 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(5).

%I A194169 #14 Nov 12 2017 03:03:54
%S A194169 0,0,1,2,2,2,3,4,4,4,5,6,6,6,7,8,8,8,8,9,10,10,11,11,12,12,13,13,14,
%T A194169 14,15,15,16,16,16,17,17,18,19,19,20,21,21,21,22,23,23,23,24,24,25,25,
%U A194169 25,26,27,27,28,28,29,30,30,31,31,32,32,32,33,33,34,34,35,36,36
%N A194169 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(5).
%H A194169 G. C. Greubel, <a href="/A194169/b194169.txt">Table of n, a(n) for n = 1..5000</a>
%t A194169 r = Sqrt[5];
%t A194169 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194169 Table[a[n], {n, 1, 90}]   (* A194169 *)
%t A194169 s[n_] := Sum[a[k], {k, 1, n}]
%t A194169 Table[s[n], {n, 1, 100}]  (* A194170 *)
%o A194169 (PARI) a(n) = floor(sum(k=1, n, frac(sqrt(5)*k))); \\ _Michel Marcus_, Nov 11 2017
%Y A194169 Cf. A194170.
%K A194169 nonn
%O A194169 1,4
%A A194169 _Clark Kimberling_, Aug 18 2011