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%I #40 Dec 26 2023 08:32:08
%S 0,1,3,5,7,10,13,16,19,22,26,30,34,38,42,46,50,55,60,65,70,75,80,85,
%T 90,95,101,107,113,119,125,131,137,143,149,155,161,168,175,182,189,
%U 196,203,210,217,224,231,238,245,252,260,268,276,284,292,300,308,316
%N a(n) = Sum_{k=0..n} ceiling(sqrt(k)).
%C Partial sums of A003059.
%C 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
%H Peter Kagey, <a href="/A327672/b327672.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = (1 + floor(sqrt(n)))*(6*n - floor(sqrt(n)) - 2*floor(sqrt(n))^2)/6. - _Vaclav Kotesovec_, Dec 26 2023
%t Accumulate[Ceiling[Sqrt[Range[0, 60]]]]
%t Table[(1 + Floor[Sqrt[n]])*(6*n - Floor[Sqrt[n]] - 2*Floor[Sqrt[n]]^2)/6, {n, 0, 100}] (* _Vaclav Kotesovec_, Dec 26 2023 *)
%Y Cf. A003059, A022554.
%K nonn
%O 0,3
%A _Peter Kagey_, Sep 21 2019
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