A014914 a(1)=1, a(n) = 25*a(n-1) + n.

1, 27, 678, 16954, 423855, 10596381, 264909532, 6622738308, 165568457709, 4139211442735, 103480286068386, 2587007151709662, 64675178792741563, 1616879469818539089, 40421986745463477240, 1010549668636586931016, 25263741715914673275417, 631593542897866831885443

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 (27,-51,25).

Crossrefs

Row n=25 of A126885.

Programs

Magma

I:=[1, 27, 678]; [n le 3 select I[n] else 27*Self(n-1) - 51*Self(n-2)+ 25*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 19 2012

Mathematica

LinearRecurrence[{27, -51, 25}, {1, 27, 678}, 20] (* Vincenzo Librandi, Oct 19 2012 *)
nxt[{n_,a_}]:={n+1,25a+n+1}; NestList[nxt,{1,1},20][[All,2]] (* Harvey P. Dale, Nov 16 2021 *)

Formula

a(1)=1, a(2)=27, a(3)=678, a(n) = 27*a(n-1) - 51*a(n-2) + 25*a(n-3). - Vincenzo Librandi, Oct 19 2012

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

G.f.: x/((1-25*x)*(x-1)^2).

E.g.f.: exp(x)*(25*exp(24*x) - 24*x - 25)/576.

a(n) = (25^(n+1) - 24*n - 25)/576. (End)