A190982 a(n) = 9*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.

0, 1, 9, 76, 639, 5371, 45144, 379441, 3189249, 26806036, 225308079, 1893742531, 15917142384, 133785568801, 1124484407289, 9451431821596, 79440464357919, 667707020113291, 5612160859230024, 47170912632503761, 396477409396383729, 3332442121404934756

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-5).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

[Round(5^((n-1)/2)*Evaluate(ChebyshevU(n), 9/(2*Sqrt(5)))): n in [0..30]]; // G. C. Greubel, Aug 26 2022

Mathematica

LinearRecurrence[{9,-5}, {0,1}, 50]

SageMath

A190982 = BinaryRecurrenceSequence(9,-5,0,1)
[A190982(n) for n in (0..30)] # G. C. Greubel, Aug 26 2022

Formula

G.f.: x/(1 - 9*x + 5*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (2/sqrt(61))*exp(9*x/2)*sinh(sqrt(61)*x/2). - G. C. Greubel, Aug 26 2022