A117617 a(n) = 5*a(n-1) + 3 with a(0) = 1.

1, 8, 43, 218, 1093, 5468, 27343, 136718, 683593, 3417968, 17089843, 85449218, 427246093, 2136230468, 10681152343, 53405761718, 267028808593, 1335144042968, 6675720214843, 33378601074218, 166893005371093

Offset: 0

Author

Parthasarathy Nambi, Apr 07 2006

Keywords

• nonn

Examples

			If n=1 then a(1) = 5*a(0) + 3 = 5*1 + 3 = 8 which is the second term.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -5).

Crossrefs

Cf. A116952.

Programs

Mathematica

a[0] := 1; a[n_] := 5*a[n - 1] + 3; Table[a[n], {n, 0, 35}] (* Stefan Steinerberger, Apr 08 2006 *)
NestList[5#+3&,1,20] (* Harvey P. Dale, Jun 14 2024 *)

Formula

G.f.: (1+2*x)/((1-x)*(1-5*x)). - Philippe Deléham, Feb 22 2014

a(n) = 6*a(n-1) - 5*a(n-2), a(0) = 1, a(1) = 8. - Philippe Deléham, Feb 22 2014

Extensions

More terms from Stefan Steinerberger, Apr 08 2006