cp's OEIS Frontend

A194161 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(2).

%I A194161 #15 Nov 08 2017 02:32:31
%S A194161 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 A194161 14,15,15,16,16,16,17,18,18,19,19,20,21,21,22,22,22,23,24,24,25,25,25,
%U A194161 26,27,27,28,28,28,29,30,30,30,31,31,32,32,33,33,34,35,35,36,36
%N A194161 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(2).
%H A194161 G. C. Greubel, <a href="/A194161/b194161.txt">Table of n, a(n) for n = 1..5000</a>
%F A194161 a(n) = [n(n+1)r] - Sum_{k=1..n} [k*r], where [ ]=floor and r=sqrt(2).
%t A194161 r = Sqrt[2];
%t A194161 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194161 Table[a[n], {n, 1, 90}]   (* A194161 *)
%t A194161 s[n_] := Sum[a[k], {k, 1, n}]
%t A194161 Table[s[n], {n, 1, 100}]  (* A194162 *)
%o A194161 (PARI) a(n) = floor(sum(k=1, n, frac(k*sqrt(2)))); \\ _Michel Marcus_, Nov 06 2017
%Y A194161 Cf. A194162.
%K A194161 nonn
%O A194161 1,4
%A A194161 _Clark Kimberling_, Aug 18 2011