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A230586
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a(n) = n^5 - 5*n^3 + 5*n.
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2
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1, 2, 123, 724, 2525, 6726, 15127, 30248, 55449, 95050, 154451, 240252, 360373, 524174, 742575, 1028176, 1395377, 1860498, 2441899, 3160100, 4037901, 5100502, 6375623, 7893624, 9687625, 11793626, 14250627, 17100748, 20389349, 24165150, 28480351, 33390752
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OFFSET
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1,2
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COMMENTS
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Numbers n such that the polynomial x^10 - n*x^5 + 1 is reducible (see paper in A231123).
Second row of A231123.
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LINKS
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Table of n, a(n) for n=1..32.
Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).
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FORMULA
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G.f.: x*(1 - 4*x + 126*x^2 - 4*x^3 + x^4)/(1 - x)^6. - Vincenzo Librandi, Jan 11 2015
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MATHEMATICA
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Table[n^5-5n^3+5n, {n, 30}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 2, 123, 724, 2525, 6726}, 30] (* Harvey P. Dale, Jan 10 2015 *)
CoefficientList[Series[(1 - 4 x + 126 x^2 - 4 x^3 + x^4) / (1 - x)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 11 2015 *)
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PROG
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(PARI) for(n=1, 10^10, if(!polisirreducible(x^10-n*x^5+1), print1(n, ", ")));
(MAGMA) [n^5 - 5*n^3 + 5*n: n in [1..40]]; // Vincenzo Librandi, Jan 11 2015
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CROSSREFS
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Cf. A230584.
Sequence in context: A249502 A249503 A249504 * A024244 A088055 A065705
Adjacent sequences: A230583 A230584 A230585 * A230587 A230588 A230589
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Oct 24 2013
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EXTENSIONS
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More terms from Vincenzo Librandi, Jan 11 2015
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STATUS
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approved
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