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

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-5).

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

Mathematica

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

Prog

(Magma) [Round(5^((n-1)/2)*Evaluate(ChebyshevU(n), 9/(2*Sqrt(5)))): n in [0..30]]; // G. C. Greubel, Aug 26 2022
(SageMath)
A190982 = BinaryRecurrenceSequence(9, -5, 0, 1)
[A190982(n) for n in (0..30)] # G. C. Greubel, Aug 26 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A319957 A056339 A056329 * A082677 A185818 A324354

Adjacent sequences: A190979 A190980 A190981 * A190983 A190984 A190985

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved