A230586 a(n) = n^5 - 5*n^3 + 5*n.

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

Offset

1,2

Comments

Numbers n such that the polynomial x^10 - n*x^5 + 1 is reducible (see paper in A231123).

Second row of A231123.

Links

Table of n, a(n) for n=1..32.

Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Formula

G.f.: x*(1 - 4*x + 126*x^2 - 4*x^3 + x^4)/(1 - x)^6. - Vincenzo Librandi, Jan 11 2015

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A230584.

Sequence in context: A249502 A249503 A249504 * A024244 A088055 A065705

Adjacent sequences: A230583 A230584 A230585 * A230587 A230588 A230589

Keyword

nonn,easy

Author

Ralf Stephan, Oct 24 2013

Extensions

More terms from Vincenzo Librandi, Jan 11 2015

Status

approved