A134547 a(n)=5n^2+20n+4.

29, 64, 109, 164, 229, 304, 389, 484, 589, 704, 829, 964, 1109, 1264, 1429, 1604, 1789, 1984, 2189, 2404, 2629, 2864, 3109, 3364, 3629, 3904, 4189, 4484, 4789, 5104

Offset

1,1

Comments

Most quintic polynomials x^5 + 5x(5*n^2+20n+4) + 8(5*n^2+20n+4) (with the exception of n=0 or 4 when the polynomial is solvable, or n=-2 when it is reducible) have nonsolvable alternating Galois group A_5 (of order 60) over rational numbers.

Links

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Formula

G.f.: -x*(29-23*x+4*x^2)/(-1+x)^3. - R. J. Mathar, Nov 14 2007

Mathematica

Table[5n^2 + 20n + 4, {n, 1, 30}]

Prog

(PARI) a(n)=5*n^2+20*n+4 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A134538.

Sequence in context: A092222 A338529 A039516 * A259636 A240169 A044131

Adjacent sequences: A134544 A134545 A134546 * A134548 A134549 A134550

Keyword

nonn,easy

Author

Artur Jasinski, Oct 31 2007, Nov 21 2007

Status

approved