A241848 a(n) = n^2 + 18.

18, 19, 22, 27, 34, 43, 54, 67, 82, 99, 118, 139, 162, 187, 214, 243, 274, 307, 342, 379, 418, 459, 502, 547, 594, 643, 694, 747, 802, 859, 918, 979, 1042, 1107, 1174, 1243, 1314, 1387, 1462, 1539, 1618, 1699, 1782, 1867, 1954, 2043, 2134, 2227, 2322, 2419, 2518

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+18: n in [0..60]];

Mathematica

Table[n^2 + 18, {n, 0, 60}]
LinearRecurrence[{3,-3,1},{18,19,22},60] (* Harvey P. Dale, Jan 18 2025 *)

PARI

a(n)=n^2+18 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (18 - 35*x + 19*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 03 2020: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(18)*Pi*coth(sqrt(18)*Pi))/36.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(18)*Pi*cosech(sqrt(18)*Pi))/36. (End)

E.g.f.: exp(x)*(18 + x + x^2). - Elmo R. Oliveira, Nov 29 2024