cp's OEIS Frontend

A194162 Partial sums of A194161.

%I A194162 #10 Nov 08 2017 11:53:29
%S A194162 0,1,2,4,6,8,11,14,18,22,27,33,39,46,53,61,69,77,86,95,105,115,126,
%T A194162 138,150,163,176,190,204,218,233,248,264,280,296,313,331,349,368,387,
%U A194162 407,428,449,471,493,515,538,562,586,611,636,661,687,714,741,769
%N A194162 Partial sums of A194161.
%H A194162 G. C. Greubel, <a href="/A194162/b194162.txt">Table of n, a(n) for n = 1..1000</a>
%t A194162 r = Sqrt[2];
%t A194162 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194162 Table[a[n], {n, 1, 90}]
%t A194162 s[n_] := Sum[a[k], {k, 1, n}]   (* A194161 *)
%t A194162 Table[s[n], {n, 1, 100}]
%t A194162 b[n_] := Floor[n (n + 1) r/2] - Sum[Floor[k*r], {k, 1, n}]
%t A194162 Table[b[n], {n, 1, 90}]   (* A194162 *)
%o A194162 (PARI) b(n) = floor(sum(k=1, n, frac(k*sqrt(2))));
%o A194162 a(n) = sum(k=1, n, b(k)); \\ _Michel Marcus_, Nov 06 2017
%Y A194162 Cf. A194161.
%K A194162 nonn
%O A194162 1,3
%A A194162 _Clark Kimberling_, Aug 18 2011