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A194204 a(n) = [Sum_{k=1..n} (k*e/2)], where [ ]=floor, ( )=fractional part.

%I A194204 #12 Nov 12 2017 03:03:16
%S A194204 0,1,1,1,2,2,3,3,4,4,5,6,6,6,7,7,7,8,9,9,9,10,11,11,12,13,13,13,14,15,
%T A194204 15,15,16,16,17,18,18,19,19,19,20,20,20,21,21,22,23,23,23,24,25,25,25,
%U A194204 26,27,27,27,28,28,29,30,30,31,32,32,33,33,33,34,34,34,35,36
%N A194204 a(n) = [Sum_{k=1..n} (k*e/2)], where [ ]=floor, ( )=fractional part.
%H A194204 G. C. Greubel, <a href="/A194204/b194204.txt">Table of n, a(n) for n = 1..5000</a>
%t A194204 r = E/2;
%t A194204 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194204 Table[a[n], {n, 1, 90}]  (* A194204 *)
%t A194204 s[n_] := Sum[a[k], {k, 1, n}]
%t A194204 Table[s[n], {n, 1, 100}] (* A194205 *)
%o A194204 (PARI) a(n) = floor(sum(k=1, n, frac(exp(1)*k/2))); \\ _Michel Marcus_, Nov 12 2017
%Y A194204 Cf. A194205.
%K A194204 nonn
%O A194204 1,5
%A A194204 _Clark Kimberling_, Aug 19 2011