A014913 a(1)=1, a(n) = 24*a(n-1) + n.

1, 26, 627, 15052, 361253, 8670078, 208081879, 4993965104, 119855162505, 2876523900130, 69036573603131, 1656877766475156, 39765066395403757, 954361593489690182, 22904678243752564383, 549712277850061545208, 13193094668401477085009, 316634272041635450040234

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 (26,-49,24).

Crossrefs

Row n=24 of A126885.

Programs

Magma

I:=[1, 26, 627]; [n le 3 select I[n] else 26*Self(n-1) - 49*Self(n-2) + 24*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 19 2012

Mathematica

LinearRecurrence[{26, -49, 24}, {1, 26, 627}, 20] (* Vincenzo Librandi, Oct 19 2012 *)
nxt[{n_,a_}]:={n+1,24a+n+1}; NestList[nxt,{1,1},20][[;;,2]] (* Harvey P. Dale, Jun 30 2025 *)

Formula

a(1)=1, a(2)=26, a(3)=627, a(n) = 26*a(n-1) - 49*a(n-2) + 24*a(n-3). - Vincenzo Librandi, Oct 19 2012

From Elmo R. Oliveira, Mar 30 2025: (Start)

G.f.: x/((1-24*x)*(x-1)^2).

E.g.f.: exp(x)*(24*exp(23*x) - 23*x - 24)/529.

a(n) = (24^(n+1) - 23*n - 24)/529. (End)