A241851 a(n) = n^2 + 21.

21, 22, 25, 30, 37, 46, 57, 70, 85, 102, 121, 142, 165, 190, 217, 246, 277, 310, 345, 382, 421, 462, 505, 550, 597, 646, 697, 750, 805, 862, 921, 982, 1045, 1110, 1177, 1246, 1317, 1390, 1465, 1542, 1621, 1702, 1785, 1870, 1957, 2046, 2137, 2230, 2325, 2422, 2521

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 sequence listed in A114962.

Programs

Magma

[n^2+21: n in [0..60]];

Mathematica

Table[n^2 + 21, {n, 0, 60}]

PARI

a(n)=n^2+21 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (21 - 41*x + 22*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(21)*Pi*coth(sqrt(21)*Pi))/42.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(21)*Pi*cosech(sqrt(21)*Pi))/42. (End)

E.g.f.: exp(x)*(21 + x + x^2). - Elmo R. Oliveira, Nov 29 2024