A241749 a(n) = n^2 + 13.

13, 14, 17, 22, 29, 38, 49, 62, 77, 94, 113, 134, 157, 182, 209, 238, 269, 302, 337, 374, 413, 454, 497, 542, 589, 638, 689, 742, 797, 854, 913, 974, 1037, 1102, 1169, 1238, 1309, 1382, 1457, 1534, 1613, 1694, 1777, 1862, 1949, 2038, 2129, 2222, 2317, 2414, 2513

Offset: 0

Author

Vincenzo Librandi, Apr 30 2014

Keywords

• nonn
• easy

Comments

For i=0..28, 2*a(i) + 3 is prime. - Vincenzo Librandi, Jun 01 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. similar sequences listed in A114962.

Programs

Magma

[n^2+13: n in [0..60]];

Mathematica

Table[n^2 + 13, {n, 0, 60}]

PARI

a(n)=n^2+13 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (13 - 25*x + 14*x^2)/(1 - x)^3.

a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.

From Amiram Eldar, Nov 02 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(13)*Pi*coth(sqrt(13)*Pi))/26.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(13)*Pi*cosech(sqrt(13)*Pi))/26. (End)

E.g.f.: exp(x)*(13 + x + x^2). - Elmo R. Oliveira, Apr 20 2025