A014900 a(1)=1, a(n) = 17*a(n-1) + n.

1, 19, 326, 5546, 94287, 1602885, 27249052, 463233892, 7874976173, 133874594951, 2275868114178, 38689757941038, 657725884997659, 11181340044960217, 190082780764323704, 3231407272993502984, 54933923640889550745, 933876701895122362683, 15875903932217080165630

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 (19,-35,17).

Crossrefs

Row n=17 of A126885.

Programs

Magma

I:=[1, 19, 326]; [n le 3 select I[n] else 19*Self(n-1) - 35*Self(n-2) + 17*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Maple

a:=n->sum((17^(n-j)-1)/16,j=0..n): seq(a(n), n=1..16); # Zerinvary Lajos, Jan 05 2007
a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,17]])^n)[2,3]:
seq(a(n), n=1..16);  # Alois P. Heinz, Aug 06 2008

Mathematica

LinearRecurrence[{19, -35, 17}, {1, 19, 326}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
nxt[{n_,a_}]:={n+1,17a+n+1}; NestList[nxt,{1,1},20][[All,2]] (* Harvey P. Dale, Jun 19 2021 *)

Formula

a(1)=1, a(2)=19, a(3)=326, a(n) = 19*a(n-1) - 35*a(n-2) + 17*a(n-3). - Vincenzo Librandi, Oct 20 2012

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

G.f.: x/((1-17*x)*(1-x)^2).

E.g.f.: exp(x)*(17*exp(16*x) - 16*x - 17)/256.

a(n) = (17^(n+1) - 16*n - 17)/256. (End)