A194164 Partial sums of A194163.

0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 48, 55, 63, 72, 81, 91, 101, 112, 123, 135, 147, 159, 171, 184, 198, 212, 227, 243, 259, 275, 292, 310, 328, 346, 365, 384, 404, 424, 445, 466, 487, 509, 532, 555, 578, 602, 627, 652, 677, 703, 730, 757, 785

Offset

1,3

Links

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

Mathematica

r = Sqrt[3];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]      (* A194163 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]     (* A194164 *)

Prog

(PARI) for(n=1, 50, print1(sum(j=1, n, floor(sum(k=1, j, frac(k*sqrt(3))))), ", ")) \\ G. C. Greubel, Oct 29 2017

Crossrefs

Cf. A194163.

Sequence in context: A194174 A168048 A075354 * A194254 A086378 A088900

Adjacent sequences: A194161 A194162 A194163 * A194165 A194166 A194167

Keyword

nonn

Author

Clark Kimberling, Aug 18 2011

Status

approved