A110831 a(n) = 3*n^2 + 27*n + 1.

31, 67, 109, 157, 211, 271, 337, 409, 487, 571, 661, 757, 859, 967, 1081, 1201, 1327, 1459, 1597, 1741, 1891, 2047, 2209, 2377, 2551, 2731, 2917, 3109, 3307, 3511, 3721, 3937, 4159, 4387, 4621, 4861, 5107, 5359, 5617, 5881, 6151, 6427, 6709, 6997, 7291

Offset

1,1

Comments

The values of a(n) for 1 <= n <= 14 are primes, a(15) = 1081 = 23*47.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Formula

From G. C. Greubel, Oct 19 2017: (Start)

G.f.: x*(31 - 24*x + x^2)/(1 - x)^3.

E.g.f.: (1 + 30*x + 3*x^2)*exp(x) - 1. (End)

Sum_{n>=1} 1/a(n) = tan(sqrt(239/3)*Pi/2)*Pi/sqrt(717) - 2643017/2948761. - Amiram Eldar, Jan 31 2023

Mathematica

Table[3*n^2 + 27*n + 1, {n, 100}]

Prog

(PARI) a(n)=3*n^2+27*n+1 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [3*n^2 + 27*n + 1: n in [1..25]]; // G. C. Greubel, Oct 19 2017

Crossrefs

Sequence in context: A044133 A044514 A142110 * A212723 A193573 A086042

Adjacent sequences: A110828 A110829 A110830 * A110832 A110833 A110834

Keyword

easy,nonn

Author

Joao da Silva (zxawyh66(AT)yahoo.com), Sep 16 2005

Extensions

Edited by Arkadiusz Wesolowski, Oct 11 2011

Status

approved