A014897 a(1)=1, a(n) = 14*a(n-1) + n.

1, 16, 227, 3182, 44553, 623748, 8732479, 122254714, 1711566005, 23961924080, 335466937131, 4696537119846, 65751519677857, 920521275490012, 12887297856860183, 180422169996042578, 2525910379944596109, 35362745319224345544, 495078434469140837635, 6931098082567971726910

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 (16,-29,14).

Crossrefs

Row n=14 of A126885.

Programs

Magma

I:=[1, 16, 227]; [n le 3 select I[n] else 16*Self(n-1) - 29*Self(n-2) + 14*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Mathematica

LinearRecurrence[{16, -29, 14}, {1, 16, 227}, 20] (* Vincenzo Librandi, Oct 20 2012 *)

Formula

a(1)=1, a(2)=16, a(3)=227, a(n) = 16*a(n-1) - 29*a(n-2) + 14*a(n-3). - Vincenzo Librandi, Oct 20 2012

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

G.f.: x/((1-14*x)*(1-x)^2).

E.g.f.: exp(x)*(14*exp(13*x) - 13*x - 14)/169.

a(n) = (14^(n+1) - 13*n - 14)/169. (End)