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A194202 a(n) = [Sum_{k=1..n} (2k*e)], where [ ]=floor, ( )=fractional part.

%I A194202 #14 Aug 16 2021 14:53:04
%S A194202 0,1,1,2,2,3,3,3,4,5,5,6,6,6,7,8,8,9,9,10,10,11,11,11,12,13,14,14,14,
%T A194202 15,15,16,16,17,18,18,18,19,19,19,20,21,21,22,22,22,23,24,24,25,25,26,
%U A194202 26,27,27,27,28,28,29,29,30,30,31,32,32,33,33,34,34,34,35,36,37
%N A194202 a(n) = [Sum_{k=1..n} (2k*e)], where [ ]=floor, ( )=fractional part.
%H A194202 G. C. Greubel, <a href="/A194202/b194202.txt">Table of n, a(n) for n = 1..5000</a>
%t A194202 r = 2E;
%t A194202 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194202 Table[a[n], {n, 1, 90}]  (* A194202 *)
%t A194202 s[n_] := Sum[a[k], {k, 1, n}]
%t A194202 Table[s[n], {n, 1, 100}] (* A194203 *)
%t A194202 Floor[Accumulate[FractionalPart[2 Range[80]E]]] (* _Harvey P. Dale_, Aug 16 2021 *)
%o A194202 (PARI) a(n) = floor(sum(k=1, n, frac(2*exp(1)*k))); \\ _Michel Marcus_, Nov 12 2017
%Y A194202 Cf. A194203.
%K A194202 nonn
%O A194202 1,4
%A A194202 _Clark Kimberling_, Aug 19 2011