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

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (9,-6).

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

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 *)

Prog

(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<x>:=PowerSeriesRing(Integers(), 22); [0] cat Coefficients(R!( x/(1-9*x+6*x^2))); // Marius A. Burtea, Jan 22 2020
(SageMath)
A190983 = BinaryRecurrenceSequence(9, -6, 0, 1)
[A190983(n) for n in (0..30)] # G. C. Greubel, Aug 26 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A210045 A125397 A095249 * A254664 A223204 A351513

Adjacent sequences: A190980 A190981 A190982 * A190984 A190985 A190986

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved