A177041 Sum(round(k^2/n),k=1..n).

1, 3, 4, 7, 11, 16, 20, 26, 31, 39, 44, 53, 63, 74, 82, 94, 105, 119, 128, 141, 157, 174, 188, 204, 221, 239, 254, 275, 295, 318, 336, 360, 377, 403, 422, 447, 475, 502, 526, 554, 581, 611, 636, 665, 697, 732, 760, 794, 825, 861

Offset: 1

Author

Mircea Merca, Dec 09 2010

Keywords

• nonn
• easy

Comments

The round function, also called the nearest integer function, is defined here by round(x)=floor(x+1/2).

Links

• Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Crossrefs

Cf. A014817.

Programs

Maple

A177041 := proc(n)
    add( round(j^2/n),j=1..n) ;
end proc:

Mathematica

Table[Sum[Floor[k^2/n + 1/2], {k, n}], {n, 50}]