A014903 a(1)=1, a(n) = 19*a(n-1) + n.

1, 21, 402, 7642, 145203, 2758863, 52418404, 995949684, 18923044005, 359537836105, 6831218886006, 129793158834126, 2466070017848407, 46855330339119747, 890251276443275208, 16914774252422228968, 321380710796022350409, 6106233505124424657789, 116018436597364068498010

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 (21,-39,19).

Crossrefs

Row n=19 of A126885.

Programs

Magma

I:=[1, 21, 402]; [n le 3 select I[n] else 21*Self(n-1) - 39*Self(n-2) + 19*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Mathematica

LinearRecurrence[{21, -39, 19}, {1, 21, 402}, 20] (* Vincenzo Librandi, Oct 20 2012 *)

Formula

a(1)=1, a(2)=21, a(3)=402, a(n) = 21*a(n-1) - 39*a(n-2) + 19*a(n-3). - Vincenzo Librandi, Oct 20 2012

From Elmo R. Oliveira, Mar 29 2025: (Start)

G.f.: x/((1-19*x)*(1-x)^2).

E.g.f.: exp(x)*(19*exp(18*x) - 18*x - 19)/324.

a(n) = (19^(n+1) - 18*n - 19)/324. (End)