A241847 a(n) = n^2 + 17.

17, 18, 21, 26, 33, 42, 53, 66, 81, 98, 117, 138, 161, 186, 213, 242, 273, 306, 341, 378, 417, 458, 501, 546, 593, 642, 693, 746, 801, 858, 917, 978, 1041, 1106, 1173, 1242, 1313, 1386, 1461, 1538, 1617, 1698, 1781, 1866, 1953, 2042, 2133, 2226, 2321, 2418, 2517

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+17: n in [0..60]];

Mathematica

Table[n^2 + 17, {n, 0, 60}]

PARI

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

Formula

G.f.: (17 - 33*x + 18*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(17)*Pi*coth(sqrt(17)*Pi))/34.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(17)*Pi*cosech(sqrt(17)*Pi))/34. (End)

E.g.f.: exp(x)*(17 + x + x^2). - Elmo R. Oliveira, Nov 29 2024