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

1,3

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A194161.

Sequence in context: A032514 A011858 A183144 * A084627 A321531 A194224

Adjacent sequences: A194159 A194160 A194161 * A194163 A194164 A194165

Keyword

nonn

Author

Clark Kimberling, Aug 18 2011

Status

approved