A014785 - OEIS

%I #17 Sep 08 2022 08:44:39

%S 1,3,6,9,13,18,24,30,35,43,52,61,69,80,92,102,113,125,140,155,169,184,

%T 202,220,231,251,270,291,309,332,354,376,397,419,446,469,493,520,550,

%U 578,601,631,660,693,721,754,788

%N a(n) = Sum_{0<=k<=n} ceiling(k^2/n).

%D M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 103.

%H Robert Israel, <a href="/A014785/b014785.txt">Table of n, a(n) for n = 1..10000</a>

%p f := n->sum( ceil(k^2/n), k=0..n);

%t Table[Sum[Ceiling[k^2/n],{k,0,n}],{n,50}] (* _Harvey P. Dale_, Oct 24 2013 *)

%o (Magma) [&+[Ceiling(k^2/n):k in [0..n]]:n in [1..50]]; // _Marius A. Burtea_, Dec 31 2019

%Y Cf. A014817 (with floor), A177041 (with round).

%K nonn

%O 1,2

%A _N. J. A. Sloane_.