A106565 a(n) = 5*a(n-1) + 5*a(n-2) with a(0) = 0, a(1) = 5.

0, 5, 25, 150, 875, 5125, 30000, 175625, 1028125, 6018750, 35234375, 206265625, 1207500000, 7068828125, 41381640625, 242252343750, 1418169921875, 8302111328125, 48601406250000, 284517587890625, 1665594970703125

Offset: 0

Author

Roger L. Bagula, May 30 2005

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A057088.

Programs

Magma

I:=[0,5]; [n le 2 select I[n] else 5*(Self(n-1) +Self(n-2)): n in [1..41]]; // G. C. Greubel, Sep 06 2021

Mathematica

LinearRecurrence[{5,5}, {0,5}, 40] (* G. C. Greubel, Sep 06 2021 *)

Sage

[5*lucas_number1(n, 5, -5) for n in (0..40)] # G. C. Greubel, Sep 06 2021

Formula

Equals 5*A057088(n). - T. D. Noe, Feb 17 2006

From Philippe Deléham, Nov 19 2008: (Start)

a(n) = 5*a(n-1) + 5*a(n-2), n > 1; a(0)=0, a(1)=5.

G.f.: 5*x/(1-5*x-5*x^2). (End)

a(n) = (1/6)*5^((n+1)/2)*((1-(-1)^n)*Lucas(2*n) + (1+(-1)^n)*sqrt(5)*Fibonacci(2*n)). - G. C. Greubel, Sep 06 2021

Extensions

Name changed by G. C. Greubel, Sep 06 2021