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

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (9,-4).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

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

Mathematica

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

SageMath

A190981 = BinaryRecurrenceSequence(9,-4,0,1)
[A190981(n) for n in (0..30)] # G. C. Greubel, Aug 25 2022

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