A190987 a(n) = 10*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.

0, 1, 10, 95, 900, 8525, 80750, 764875, 7245000, 68625625, 650031250, 6157184375, 58321687500, 552430953125, 5232701093750, 49564856171875, 469485056250000, 4447026281640625, 42122837535156250, 398993243943359375, 3779318251757812500, 35798216297861328125

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-5).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Cf. A019934 (sqrt(5-2*sqrt(5))), A019952 (sqrt(5+2*sqrt(5))).

Programs

Magma

[Round(5^((n-1)/2)*Evaluate(ChebyshevU(n), Sqrt(5))): n in [0..30]]; // G. C. Greubel, Sep 07 2022

Mathematica

LinearRecurrence[{10,-5}, {0,1}, 50]

SageMath

A190987 = BinaryRecurrenceSequence(10, -5, 0, 1)
[A190987(n) for n in (0..30)] # G. C. Greubel, Sep 07 2022

Formula

G.f.: x/(1 - 10*x + 5*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (1/(2*sqrt(5)))*exp(5*x)*sinh(2*sqrt(5)*x). - G. C. Greubel, Sep 07 2022