A194161 - OEIS

%I #15 Nov 08 2017 02:32:31

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

%T 14,15,15,16,16,16,17,18,18,19,19,20,21,21,22,22,22,23,24,24,25,25,25,

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

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

%H G. C. Greubel, <a href="/A194161/b194161.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = [n(n+1)r] - Sum_{k=1..n} [k*r], where [ ]=floor and r=sqrt(2).

%t r = Sqrt[2];

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

%t Table[a[n], {n, 1, 90}]   (* A194161 *)

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

%t Table[s[n], {n, 1, 100}]  (* A194162 *)

%o (PARI) a(n) = floor(sum(k=1, n, frac(k*sqrt(2)))); \\ _Michel Marcus_, Nov 06 2017

%Y Cf. A194162.

%K nonn

%O 1,4

%A _Clark Kimberling_, Aug 18 2011