A241890 a(n) = n^2 + 24.

24, 25, 28, 33, 40, 49, 60, 73, 88, 105, 124, 145, 168, 193, 220, 249, 280, 313, 348, 385, 424, 465, 508, 553, 600, 649, 700, 753, 808, 865, 924, 985, 1048, 1113, 1180, 1249, 1320, 1393, 1468, 1545, 1624, 1705, 1788, 1873, 1960, 2049, 2140, 2233, 2328, 2425, 2524

Offset: 0

Author

Vincenzo Librandi, May 01 2014

Keywords

• nonn
• easy

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+24: n in [0..60]];

Mathematica

Table[n^2 + 24, {n, 0, 60}]
LinearRecurrence[{3,-3,1},{24,25,28},60] (* Harvey P. Dale, Jun 24 2025 *)

PARI

a(n)=n^2+24 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (24 - 47*x + 25*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 04 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(24)*Pi*coth(sqrt(24)*Pi))/48.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(24)*Pi*cosech(sqrt(24)*Pi))/48. (End)

E.g.f.: exp(x)*(24 + x + x^2). - Elmo R. Oliveira, Nov 29 2024