A190983 a(n) = 9*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.

0, 1, 9, 75, 621, 5139, 42525, 351891, 2911869, 24095475, 199388061, 1649919699, 13652948925, 112977022131, 934875505629, 7736017417875, 64014903727101, 529718029036659, 4383372838967325, 36272047376485971, 300148189354569789, 2483701419932212275

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (9,-6).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

[n le 2 select n-1 else 9*Self(n-1) - 6*Self(n-2):n in [1..22]]; // Marius A. Burtea, Jan 22 2020

Magma

R:=PowerSeriesRing(Integers(), 22); [0] cat Coefficients(R!( x/(1-9*x+6*x^2))); // Marius A. Burtea, Jan 22 2020

Mathematica

LinearRecurrence[{9,-6}, {0,1}, 50]
With[{s=Sqrt[57]},Table[Simplify[(2^(-1-x) (4s (9+s)^x-(9-s)^x (171+ 23s)))/ (57(9+s))],{x,30}]] (* Harvey P. Dale, Sep 01 2014 *)

SageMath

A190983 = BinaryRecurrenceSequence(9,-6,0,1)
[A190983(n) for n in (0..30)] # G. C. Greubel, Aug 26 2022

Formula

G.f.: x/(1-9*x+6*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (2/sqrt(57))*exp(9*x/2)*sinh(sqrt(57)*x/2). - G. C. Greubel, Aug 26 2022