A190970 a(n) = 5*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.

0, 1, 5, 16, 35, 31, -160, -1079, -3955, -10064, -14725, 16951, 217280, 933841, 2713685, 5163856, 1396115, -39494129, -210035680, -694731239, -1583335075, -1664094224, 5929544555, 44624570791, 169756952960, 447163627681, 708005561765, -484444840304

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-9).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

[n le 2 select n-1 else 5*Self(n-1) - 9*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 09 2022

Maple

A190970 := proc(n)
    option remember ;
    if n <= 1 then
        n;
    else
        5*procname(n-1)-9*procname(n-2) ;
    end if;
end proc: # R. J. Mathar, Mar 23 2023

Mathematica

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

Sage

[3^(n-1)*chebyshev_U(n-1, 5/6) for n in (0..50)] # G. C. Greubel, Jun 09 2022

Formula

G.f.: x/(1 - 5*x + 9*x^2). - Philippe Deléham, Oct 12 2011

a(n) = 3^(n-1) * ChebyshevU(n-1, 5/6). - G. C. Greubel, Jun 09 2022