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A138357 Floor of sum of the first n^2 square roots. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 21:31 EDT 2018. Contains 316404 sequences. (Running on oeis4.)