A190986 a(n) = 10*a(n-1) - 4*a(n-2), with a(0)=0, a(1)=1.

0, 1, 10, 96, 920, 8816, 84480, 809536, 7757440, 74336256, 712332800, 6825982976, 65410498560, 626801053696, 6006368542720, 57556481212416, 551539337953280, 5285167454683136, 50645517195018240, 485314502131449856, 4650562952534425600, 44564371516818456576

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,-4).
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Cf. A004254, A049310.

Programs

Magma

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

Mathematica

LinearRecurrence[{10,-4}, {0,1}, 50]

SageMath

A190986 = BinaryRecurrenceSequence(10, -4, 0, 1)
[A190986(n) for n in (0..30)] # G. C. Greubel, Sep 03 2022

Formula

G.f.: x/(1 - 10*x + 4*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (1/sqrt(21))*exp(5*x)*sinh(sqrt(21)*x). - G. C. Greubel, Sep 03 2022

a(n) = 2^(n-1)*S(n-1, 5), with the Chebyshev S-polynomial (see A049310) S(n-1, 5) = A004254(n). See the Magma program by G. C. Greubel. - Wolfdieter Lang, Nov 15 2023