A014904 a(1)=1, a(n) = 20*a(n-1) + n.

1, 22, 443, 8864, 177285, 3545706, 70914127, 1418282548, 28365650969, 567313019390, 11346260387811, 226925207756232, 4538504155124653, 90770083102493074, 1815401662049861495, 36308033240997229916, 726160664819944598337, 14523213296398891966758, 290464265927977839335179

Offset: 1

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (22,-41,20).

Crossrefs

Row n=20 of A126885.

Programs

Magma

I:=[1, 22, 443]; [n le 3 select I[n] else 22*Self(n-1) - 41*Self(n-2) + 20*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Mathematica

LinearRecurrence[{22, -41, 20}, {1, 22, 443}, 20] (* Vincenzo Librandi, Oct 20 2012 *)

Maxima

a[1]:1$
a[2]:22$
a[3]:443$
a[n]:=22*a[n-1]-41*a[n-2]+20*a[n-3]$
A014904(n):=a[n]$
makelist(A014904(n),n,1,30); /* Martin Ettl, Nov 06 2012 */

PARI

Vec(x/((1-20*x)*(x-1)^2)+O(x^99)) \\ Charles R Greathouse IV, Jul 05 2024

Formula

From R. J. Mathar, Jul 15 2010: (Start)

G.f.: x/((1-20*x)*(x-1)^2).

a(n) = 22*a(n-1) - 41*a(n-2) + 20*a(n-3). (End)

From Elmo R. Oliveira, Mar 31 2025: (Start)

E.g.f.: exp(x)*(20*exp(19*x) - 19*x - 20)/361.

a(n) = (20^(n+1) - 19*n - 20)/361. (End)