A190988 a(n) = 10*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.

0, 1, 10, 94, 880, 8236, 77080, 721384, 6751360, 63185296, 591344800, 5534336224, 51795293440, 484746917056, 4536697409920, 42458492596864, 397364741509120, 3718896459510016, 34804776146045440, 325734382703394304, 3048515170157670400, 28530745405356338176

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 (10,-6).

Formula

G.f.: x/(1-10*x+6*x^2). - Philippe Deléham, Oct 12 2011

From G. C. Greubel, Sep 15 2022: (Start)

a(n) = 6^((n-1)/2) * ChebyshevU(n-1, 5/sqrt(6)).

E.g.f.: (1/sqrt(19))*exp(5*x)*sinh(sqrt(19)*x). (End)

Mathematica

LinearRecurrence[{10, -6}, {0, 1}, 50]

Prog

(Magma) [Round(6^((n-1)/2)*Evaluate(ChebyshevU(n), 5/Sqrt(6))): n in [0..30]]; // G. C. Greubel, Sep 15 2022
(SageMath)
A190988 = BinaryRecurrenceSequence(10, -6, 0, 1)
[A190988(n) for n in (0..30)] # G. C. Greubel, Sep 15 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A369335 A126633 A125422 * A287830 A259289 A163738

Adjacent sequences: A190985 A190986 A190987 * A190989 A190990 A190991

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved