A183140 a(n) = [1/s]+[2/s]+...+[n/s], where s=2+sqrt(2) and []=floor.

0, 0, 0, 1, 2, 3, 5, 7, 9, 11, 14, 17, 20, 24, 28, 32, 36, 41, 46, 51, 57, 63, 69, 76, 83, 90, 97, 105, 113, 121, 130, 139, 148, 157, 167, 177, 187, 198, 209, 220, 232, 244, 256, 268, 281, 294, 307, 321, 335, 349, 363, 378, 393, 408

Offset: 0

Author

Clark Kimberling, Dec 26 2010

Keywords

• nonn

Comments

A183139(n) + a(n) = A000217(n) (the triangular numbers).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A183139, A000217.

Programs

Mathematica

Accumulate[Floor[Range[60]/(2+Sqrt[2])]] (* Harvey P. Dale, Oct 20 2017 *)

PARI

default(realprecision,100); s=2+sqrt(2); for(n=1,99,print1(sum(k=1,n,floor(k/s)),", "))

Formula

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