A194162 Partial sums of A194161.

0, 1, 2, 4, 6, 8, 11, 14, 18, 22, 27, 33, 39, 46, 53, 61, 69, 77, 86, 95, 105, 115, 126, 138, 150, 163, 176, 190, 204, 218, 233, 248, 264, 280, 296, 313, 331, 349, 368, 387, 407, 428, 449, 471, 493, 515, 538, 562, 586, 611, 636, 661, 687, 714, 741, 769

Offset: 1

Author

Clark Kimberling, Aug 18 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A194161.

Programs

Mathematica

r = Sqrt[2];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]
s[n_] := Sum[a[k], {k, 1, n}]   (* A194161 *)
Table[s[n], {n, 1, 100}]
b[n_] := Floor[n (n + 1) r/2] - Sum[Floor[k*r], {k, 1, n}]
Table[b[n], {n, 1, 90}]   (* A194162 *)

PARI

b(n) = floor(sum(k=1, n, frac(k*sqrt(2))));
a(n) = sum(k=1, n, b(k)); \\ Michel Marcus, Nov 06 2017