A241849 a(n) = n^2 + 19.

19, 20, 23, 28, 35, 44, 55, 68, 83, 100, 119, 140, 163, 188, 215, 244, 275, 308, 343, 380, 419, 460, 503, 548, 595, 644, 695, 748, 803, 860, 919, 980, 1043, 1108, 1175, 1244, 1315, 1388, 1463, 1540, 1619, 1700, 1783, 1868, 1955, 2044, 2135, 2228, 2323, 2420, 2519

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+19: n in [0..60]];

Maple

A241849:=n->n^2+19: seq(A241849(n), n=0..100); # Wesley Ivan Hurt, Jan 16 2017

Mathematica

Table[n^2 + 19, {n, 0, 60}]
LinearRecurrence[{3,-3,1},{19,20,23},50] (* Harvey P. Dale, Dec 05 2018 *)

PARI

a(n)=n^2+19 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (19 - 37*x + 20*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(19)*Pi*coth(sqrt(19)*Pi))/38.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(19)*Pi*cosech(sqrt(19)*Pi))/38. (End)

E.g.f.: exp(x)*(19 + x + x^2). - Elmo R. Oliveira, Nov 29 2024