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A164577
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Integer averages of the first perfect cubes up to some n^3.
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3
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1, 12, 25, 45, 112, 162, 225, 396, 507, 637, 960, 1156, 1377, 1900, 2205, 2541, 3312, 3750, 4225, 5292, 5887, 6525, 7936, 8712, 9537, 11340, 12321, 13357, 15600, 16810, 18081, 20812, 22275, 23805, 27072, 28812, 30625, 34476, 36517, 38637, 43120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Integers of the form A000537(k)/k, created by the k>0 listed in A042965. [R. J. Mathar, Aug 20 2009]
Also, integers of the form (1/4)*n*(n+1)^2 for some n. [From Zak Seidov (zakseidov(AT)yahoo.com), Aug 17 2009]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).
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FORMULA
| G.f. ( x*(1+11*x+13*x^2+17*x^3+34*x^4+11*x^5+6*x^6+3*x^7) ) / ( (1+x+x^2)^3*(x-1)^4 ). - R. J. Mathar, Jan 25 2011
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EXAMPLE
| The average of the first cube is 1^3/1=1=a(1).
The average of the first two cubes is (1^3+2^3)/2=9/2, not integer, and does not contribute to the sequence.
The average of the first three cubes is (1^3+2^3+3^3)/3=12, integer, and defines a(2).
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MATHEMATICA
| Timing[s=0; lst={}; Do[a=(s+=n^3)/n; If[Mod[a, 1]==0, AppendTo[lst, a]], {n, 5!}]; lst]
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CROSSREFS
| Cf. A050248, A051456, A078617, A078618, A154293, A164576
Sequence in context: A042851 A041280 A132754 * A195143 A198274 A175523
Adjacent sequences: A164574 A164575 A164576 * A164578 A164579 A164580
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KEYWORD
| nonn,easy
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 16 2009
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EXTENSIONS
| Changed comments to examples - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 20 2009
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