A014905 a(1)=1, a(n) = 21*a(n-1) + n.

1, 23, 486, 10210, 214415, 4502721, 94557148, 1985700116, 41699702445, 875693751355, 18389568778466, 386180944347798, 8109799831303771, 170305796457379205, 3576421725604963320, 75104856237704229736, 1577201980991788824473, 33121241600827565313951, 695546073617378871592990

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 (23,-43,21).

Crossrefs

Row n=21 of A126885.

Programs

Magma

I:=[1, 23, 486]; [n le 3 select I[n] else 23*Self(n-1) - 43*Self(n-2)+ 21*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 19 2012

Mathematica

LinearRecurrence[{23, -43, 21}, {1, 23, 486}, 20] (* Vincenzo Librandi, Oct 19 2012 *)

Formula

a(1)=1, a(2)=23, a(3)=486, a(n) = 23*a(n-1) - 43*a(n-2) + 21*a(n-3). - Vincenzo Librandi, Oct 19 2012

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

G.f.: x/((1-21*x)*(x-1)^2).

E.g.f.: exp(x)*(21*exp(20*x) - 20*x - 21)/400.

a(n) = (21^(n+1) - 20*n - 21)/400. (End)