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

Author

Clark Kimberling, Aug 18 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A194163.

Programs

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 *)

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