A190971 a(n) = 5*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=1.

0, 1, 5, 15, 25, -25, -375, -1625, -4375, -5625, 15625, 134375, 515625, 1234375, 1015625, -7265625, -46484375, -159765625, -333984375, -72265625, 2978515625, 15615234375, 48291015625, 85302734375, -56396484375, -1135009765625, -5111083984375, -14205322265625

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• sign

Links

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

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

[n le 2 select n-1 else 5*(Self(n-1) - 2*Self(n-2)): n in [1..51]]; // G. C. Greubel, Jun 10 2022

Mathematica

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

PARI

concat(0, Vec(x/(1-5*x+10*x^2) + O(x^100))) \\ Altug Alkan, Nov 26 2015

Sage

[lucas_number1(n,5,10) for n in (0..50)] # G. C. Greubel, Jun 10 2022

Formula

a(n) = (i/sqrt(15))*(((5 - i*sqrt(15))/2)^n - ((5 + i*sqrt(15))/2)^n). - Giorgio Balzarotti, May 28 2011

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

From G. C. Greubel, Jun 10 2022: (Start)

a(n) = 10^((n-1)/2) * ChebyshevU(n-1, sqrt(10)/4).

E.g.f.: (2/sqrt(15))*exp(5*x/2)*sin(sqrt(15)*x/2). (End)