A183139 a(n) = [1/r]+[2/r]+...+[n/r], where r=sqrt(2) and []=floor.

0, 1, 3, 5, 8, 12, 16, 21, 27, 34, 41, 49, 58, 67, 77, 88, 100, 112, 125, 139, 153, 168, 184, 200, 217, 235, 254, 273, 293, 314, 335, 357, 380, 404, 428, 453, 479, 505, 532, 560, 588, 617, 647, 678, 709, 741, 774, 807, 841, 876

Offset: 1

Author

Clark Kimberling, Dec 26 2010

Keywords

• nonn

Comments

A183139 + A183140 = A000217 (the triangular numbers).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A183139, A183140, A000217.

Programs

Magma

[(&+[Floor(k/Sqrt(2)):k in [1..n]]): n in [1..100]]; // G. C. Greubel, Apr 10 2018

Mathematica

Accumulate[Floor[Range[100]/(Sqrt[2])]] (* G. C. Greubel, Apr 10 2018 *)

PARI

for(n=1, 100, print1(sum(k=1,n, floor(k/sqrt(2))), ", ")) \\ G. C. Greubel, Apr 10 2018

Formula

a(n) = [1/r]+[2/r]+...+[n/r], where r=sqrt(2) and []=floor.