A014785 a(n) = Sum_{0<=k<=n} ceiling(k^2/n).

1, 3, 6, 9, 13, 18, 24, 30, 35, 43, 52, 61, 69, 80, 92, 102, 113, 125, 140, 155, 169, 184, 202, 220, 231, 251, 270, 291, 309, 332, 354, 376, 397, 419, 446, 469, 493, 520, 550, 578, 601, 631, 660, 693, 721, 754, 788

Offset

1,2

References

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

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

Mathematica

Table[Sum[Ceiling[k^2/n], {k, 0, n}], {n, 50}] (* Harvey P. Dale, Oct 24 2013 *)

Prog

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

Crossrefs

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

Sequence in context: A143975 A005488 A048202 * A132352 A033436 A059293

Adjacent sequences: A014782 A014783 A014784 * A014786 A014787 A014788

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved