A076808 a(n) = 82n^3 - 1228n^2 + 6130n - 5861.

-5861, -877, 2143, 3691, 4259, 4339, 4423, 5003, 6571, 9619, 14639, 22123, 32563, 46451, 64279, 86539, 113723, 146323, 184831, 229739, 281539, 340723, 407783, 483211, 567499, 661139, 764623, 878443, 1003091, 1139059, 1286839, 1446923, 1619803, 1805971

Offset: 0

Author

Hilko Koning (hilko(AT)hilko.net), Nov 18 2002

Keywords

• easy
• sign

Comments

A prime-generating cubic polynomial.

For n=0 ... 31, the absolute value of terms in this sequence are primes. This is not the case for n=32. See A272323 and A272324. - Robert Price, Apr 25 2016

Links

• Eric Weisstein's World of Mathematics, Prime-Generating Polynomials
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A050266, A076809, A272323, A272324.

Programs

Mathematica

Table[82 n^3 - 1228 n^2 + 6130 n - 5861, {n, 0, 31}] (* or *)
CoefficientList[Series[(13301 x^3 - 29515 x^2 + 22567 x - 5861)/(x - 1)^4, {x, 0, 31}], x] (* Michael De Vlieger, Apr 25 2016 *)
LinearRecurrence[{4,-6,4,-1},{-5861,-877,2143,3691},40] (* Harvey P. Dale, Jun 18 2018 *)

Maxima

A076808(n):=82*n^3-1228*n^2+6130*n-5861$
makelist(A076808(n),n,0,30); /* Martin Ettl, Nov 08 2012 */

PARI

a(n)=82*n^3-1228*n^2+6130*n-5861 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (13301*x^3-29515*x^2+22567*x-5861)/(x-1)^4. - Colin Barker, Nov 10 2012

E.g.f.: (-5861 + 4984*x - 982*x^2 + 82*x^3)*exp(x). - Ilya Gutkovskiy, Apr 25 2016