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A164619
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Integers of the form A164577(k)/3.
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0
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4, 15, 54, 75, 132, 169, 320, 459, 735, 847, 1104, 1250, 1764, 2175, 2904, 3179, 3780, 4107, 5200, 6027, 7425, 7935, 9024, 9604, 11492, 12879, 15162, 15979, 17700, 18605, 21504, 23595, 26979, 28175, 30672, 31974, 36100, 39039, 43740, 45387, 48804
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OFFSET
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1,1
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COMMENTS
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The sequence members are the third of the average of a set of smallest cubes, if integer.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1,2,-4,2,2,-4,2,-1,2,-1,-1,2,-1).
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FORMULA
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a(n)= +2*a(n-1) -a(n-2) -a(n-3) +2*a(n-4) -a(n-5) +2*a(n-6) -4*a(n-7) +2*a(n-8) +2*a(n-9) -4*a(n-10) +2*a(n-11) -a(n-12) +2*a(n-13) -a(n-14) -a(n-15) +2*a(n-16) -a(n-17). - R. J. Mathar, Jan 25 2011
G.f.: x*(x^14 +x^13 +16*x^12 +10*x^11 +47*x^10 -22*x^9 +61*x^8 +10*x^7 +88*x^6 +8*x^5 +43*x^4 -14*x^3 +28*x^2 +7*x +4) / ((x -1)^4*(x +1)^3*(x^2 -x +1)^3*(x^2 +x +1)^2). - Colin Barker, Oct 27 2014
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EXAMPLE
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A third of the average of the first cube, A164577(1)/3=1/3, is not integer and does not contribute to the sequence.
A third of the average of the first two cubes, A164577(2)/3=4, is integer and defines a(1)=4 of the sequence.
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MATHEMATICA
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s=0; lst={}; Do[a=(s+=(n^3)/3)/n; If[Mod[a, 1]==0, AppendTo[lst, a]], {n, 2*5!}]; lst
LinearRecurrence[{2, -1, -1, 2, -1, 2, -4, 2, 2, -4, 2, -1, 2, -1, -1, 2, -1}, {4, 15, 54, 75, 132, 169, 320, 459, 735, 847, 1104, 1250, 1764, 2175, 2904, 3179, 3780}, 50] (* Harvey P. Dale, Apr 06 2016 *)
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PROG
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(PARI) Vec(x*(x^14 +x^13 +16*x^12 +10*x^11 +47*x^10 -22*x^9 +61*x^8 +10*x^7 +88*x^6 +8*x^5 +43*x^4 -14*x^3 +28*x^2 +7*x +4) / ((x -1)^4*(x +1)^3*(x^2 -x +1)^3*(x^2 +x +1)^2) + O(x^100)) \\ Colin Barker, Oct 27 2014
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CROSSREFS
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Cf. A050248, A051456, A078617, A078618, A136116, A154293, A164286, A164576, A164577, A164578, A164579.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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