A190981 a(n) = 9*a(n-1) - 4*a(n-2), with a(0)=0, a(1)=1.

0, 1, 9, 77, 657, 5605, 47817, 407933, 3480129, 29689429, 253284345, 2160801389, 18434075121, 157263470533, 1341634934313, 11445660526685, 97644405002913, 833017002919477, 7106575406263641, 60627110644694861, 517217694177199185, 4412450805016013221

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,-4).

Formula

G.f.: x/(1-9x+4*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (2/sqrt(65))*exp(9*x/2)*sinh(sqrt(65)*x/2). - G. C. Greubel, Aug 25 2022

Mathematica

LinearRecurrence[{9, -4}, {0, 1}, 50]

Prog

(Magma) [2^(n-1)*Evaluate(ChebyshevU(n), 9/4): n in [0..30]]; // G. C. Greubel, Aug 25 2022
(SageMath)
A190981 = BinaryRecurrenceSequence(9, -4, 0, 1)
[A190981(n) for n in (0..30)] # G. C. Greubel, Aug 25 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A266125 A290708 A126631 * A254659 A346847 A355372

Adjacent sequences: A190978 A190979 A190980 * A190982 A190983 A190984

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved