A327672 a(n) = Sum_{k=0..n} ceiling(sqrt(k)).

0, 1, 3, 5, 7, 10, 13, 16, 19, 22, 26, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 260, 268, 276, 284, 292, 300, 308, 316

Offset: 0

Author

Peter Kagey, Sep 21 2019

Keywords

• nonn

Comments

Partial sums of A003059.

Given a digraph whose vertices are numbered from 0 to n and in which an edge (u,v) exists iff u < v, a(n) is the maximum number of arcs that can be chosen so that for each vertex j other than 0 and n, the number of chosen arcs whose tail is vertex j equals the number of chosen arcs whose head is vertex j. - Xutong Ding, Dec 12 2023

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003059, A022554.

Programs

Mathematica

Accumulate[Ceiling[Sqrt[Range[0, 60]]]]
Table[(1 + Floor[Sqrt[n]])*(6*n - Floor[Sqrt[n]] - 2*Floor[Sqrt[n]]^2)/6, {n, 0, 100}] (* Vaclav Kotesovec, Dec 26 2023 *)

Formula

a(n) = (1 + floor(sqrt(n)))*(6*n - floor(sqrt(n)) - 2*floor(sqrt(n))^2)/6. - Vaclav Kotesovec, Dec 26 2023