A190985 a(n) = 10*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.

0, 1, 10, 97, 940, 9109, 88270, 855373, 8288920, 80323081, 778364050, 7542671257, 73091620420, 708288190429, 6863607043030, 66511205859013, 644521237461040, 6245678757033361, 60523223857950490, 586495202308404817, 5683382351510196700, 55074337908176752549

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-3).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

[Round(3^((n-1)/2)*Evaluate(ChebyshevU(n), 5/Sqrt(3))): n in [0..30]]; // G. C. Greubel, Sep 03 2022

Mathematica

LinearRecurrence[{10,-3}, {0,1}, 50]

SageMath

A190985 = BinaryRecurrenceSequence(10, -3, 0, 1)
[A190985(n) for n in (0..30)] # G. C. Greubel, Sep 03 2022

Formula

G.f.: x/(1-10x+3*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (1/sqrt(22))*exp(5*x)*sinh(sqrt(22)*x). - G. C. Greubel, Sep 03 2022