A138357 Floor of sum of the first n^2 square roots.

0, 1, 6, 19, 44, 85, 146, 231, 345, 490, 671, 892, 1157, 1470, 1836, 2257, 2738, 3283, 3896, 4581, 5343, 6184, 7109, 8122, 9227, 10428, 11730, 13135, 14648, 16273, 18014, 19875, 21861, 23974, 26219, 28600, 31121, 33786, 36600, 39565, 42686, 45967

Offset

0,3

Comments

a(n)-A005900(n)={0,0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,...}

Links

Table of n, a(n) for n=0..41.

Mathematica

A[n_]:=Floor[HarmonicNumber[n^2, -1/2]] (* or *) A[n_]:=Floor[(2/3)n^3+n/2+1/(24n)+Zeta[ -1/2]]
nn=50; With[{c=Sqrt[Range[nn^2]]}, Table[Floor[Total[Take[c, n^2]]], {n, 0, nn}]] (* Harvey P. Dale, Apr 21 2012 *)

Prog

(PARI) a(n)=floor(sum(x=0, n^2, sqrt(x)))

Crossrefs

Cf. A005900 (Octahedral numbers:(2n^3+n)/3).

Sequence in context: A035495 A061293 A005900 * A299264 A183763 A209403

Adjacent sequences: A138354 A138355 A138356 * A138358 A138359 A138360

Keyword

nonn

Author

Zak Seidov, Mar 16 2008

Status

approved