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Search: id:A138357
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| A138357 |
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Floor of sum of the first n^2 square roots. |
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+0
1
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| 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
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OFFSET
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0,3
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COMMENT
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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,...}
A005900 Octahedral numbers:(2n^3+n)/3.
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FORMULA
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(PARI) a(n)=floor(sum(x=0,n^2,sqrt(x)))
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MATHEMATICA
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A[n_]:=Floor[HarmonicNumber[n^2, -1/2]] (* or *) A[n_]:=Floor[(2/3)n^3+n/2+1/(24n)+Zeta[ -1/2]]
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CROSSREFS
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Cf. A005900.
Sequence in context: A035495 A061293 A005900 this_sequence A005712 A070893 A027963
Adjacent sequences: A138354 A138355 A138356 this_sequence A138358 A138359 A138360
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Mar 16 2008
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