A014898 a(1)=1, a(n) = 15*a(n-1) + n.

1, 17, 258, 3874, 58115, 871731, 13075972, 196139588, 2942093829, 44131407445, 661971111686, 9929566675302, 148943500129543, 2234152501943159, 33512287529147400, 502684312937211016, 7540264694058165257, 113103970410872478873, 1696559556163087183114, 25448393342446307746730

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 (17,-31,15).

Crossrefs

Row n=15 of A126885.

Programs

Magma

I:=[1, 17, 258]; [n le 3 select I[n] else 17*Self(n-1) - 31*Self(n-2) + 15*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Mathematica

LinearRecurrence[{17, -31, 15}, {1, 17, 258}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
nxt[{n_,a_}]:={n+1,15a+n+1}; NestList[nxt,{1,1},20][[;;,2]] (* Harvey P. Dale, Jun 15 2025 *)

Formula

a(n) = 17*a(n-1) - 31*a(n-2) + 15*a(n-3); a(1)=1, a(2)=17, a(3)=258. - Vincenzo Librandi, Oct 20 2012

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

G.f.: x/((1-15*x)*(1-x)^2).

E.g.f.: exp(x)*(15*exp(14*x) - 14*x - 15)/196.

a(n) = (15^(n+1) - 14*n - 15)/196. (End)