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a(n) = [Sum_{k=1..n} (k*Pi/2)], where [ ]=floor, ( )=fractional part.
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%I #10 Apr 10 2021 02:02:55

%S 0,0,1,1,2,2,3,4,4,5,5,6,6,7,8,8,9,9,10,10,11,12,12,13,13,14,14,15,16,

%T 16,17,17,18,18,19,20,20,20,21,22,22,23,23,24,24,25,25,26,27,27,27,28,

%U 28,29,30,30,31,31,32,32,33,33,34,35,35,36,36,37,37,38,38,39

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

%t r = Pi/2;

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

%t Table[a[n], {n, 1, 90}] (* A194208 *)

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

%t Table[s[n], {n, 1, 100}] (* A194209 *)

%o (PARI) a(n) = floor(sum(k=1, n, frac(k*Pi/2))); \\ _Michel Marcus_, Apr 10 2021

%Y Cf. A194209.

%K nonn

%O 1,5

%A _Clark Kimberling_, Aug 19 2011