A194202 - OEIS

%I #14 Aug 16 2021 14:53:04

%S 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 15,15,16,16,17,18,18,18,19,19,19,20,21,21,22,22,22,23,24,24,25,25,26,

%U 26,27,27,27,28,28,29,29,30,30,31,32,32,33,33,34,34,34,35,36,37

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

%H G. C. Greubel, <a href="/A194202/b194202.txt">Table of n, a(n) for n = 1..5000</a>

%t r = 2E;

%t a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]

%t Table[a[n], {n, 1, 90}]  (* A194202 *)

%t s[n_] := Sum[a[k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}] (* A194203 *)

%t Floor[Accumulate[FractionalPart[2 Range[80]E]]] (* _Harvey P. Dale_, Aug 16 2021 *)

%o (PARI) a(n) = floor(sum(k=1, n, frac(2*exp(1)*k))); \\ _Michel Marcus_, Nov 12 2017

%Y Cf. A194203.

%K nonn

%O 1,4

%A _Clark Kimberling_, Aug 19 2011