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A144928
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Values of k arising in A144927.
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4
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49, 5341, 587461, 64615369, 7107103129, 781716728821, 85981733067181, 9457208920661089, 1040206999539652609, 114413312740441125901, 12584424194448984196501, 1384172248076647820489209, 152246362864236811269616489, 16745715742817972591837324581
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OFFSET
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1,1
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COMMENTS
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Numbers k such that there exists x in N : (x+7)^3-x^3=k^2. - Richard Choulet, Oct 16 2008
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LINKS
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FORMULA
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G.f.: 49*x*(1-x) / (1-110*x+x^2). - Colin Barker, Oct 17 2014, corrected Jul 16 2016
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EXAMPLE
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a(1) = 49 because (7+7)^3 - 7^3 = 2041 = 49^2. - Richard Choulet, Oct 16 2008
a(2) = 5341 because (1162+7)^3 - 1162^3 = 28526281 = 5341^2. - Colin Barker, Jul 16 2016
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MATHEMATICA
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Sqrt[(# + 7)^3 - #^3] & /@ Rest@ CoefficientList[Series[7 x (-1 - 55 x + 2 x^2)/((x - 1) (x^2 - 110 x + 1)), {x, 0, 14}], x] (* or *)
Rest@ CoefficientList[Series[49 x (1 - x)/(1 - 110 x + x^2), {x, 0, 14}], x] (* Michael De Vlieger, Jul 17 2016 *)
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PROG
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(PARI) Vec(49*x*(1-x)/(1-110*x+x^2) + O(x^20)) \\ Colin Barker, Oct 17 2014, corrected Jul 16 2016
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CROSSREFS
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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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All terms except the first corrected by Colin Barker, Jul 16 2016
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STATUS
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approved
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