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

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (19,-35,17).

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A143699 A015676 A098304 * A121324 A093973 A345963

Adjacent sequences: A014897 A014898 A014899 * A014901 A014902 A014903

Keyword

nonn

Author

N. J. A. Sloane, Olivier Gérard

Status

approved