A163305 Numerators of fractions in the approximation of the square root of 5 satisfying: a(n)= (a(n-1)+ c)/(a(n-1)+1); with c=5 and a(1)=0. Also product of the powers of two and five times the Fibonacci numbers.

0, 5, 10, 40, 120, 400, 1280, 4160, 13440, 43520, 140800, 455680, 1474560, 4771840, 15441920, 49971200, 161710080, 523304960, 1693450240, 5480120320, 17734041600, 57388564480, 185713295360, 600980848640, 1944814878720

Offset: 1

Author

Mark Dols, Jul 24 2009

Keywords

• nonn
• easy

Comments

For denominators see: A084057 (= product of Lucas numbers (excluding first number (2)), and powers of 2).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,4).

Crossrefs

Cf. A000032, A000079, A084057, A000045.

Programs

Mathematica

LinearRecurrence[{2,4},{0,5},30] (* Harvey P. Dale, Mar 01 2016 *)

PARI

a(n)=5*fibonacci(n-1)*2^(n-2) \\ Franklin T. Adams-Watters, Aug 06 2009

Formula

From Colin Barker, Jun 20 2012: (Start)

a(n) = 2*a(n-1) + 4*a(n-2).

G.f.: 5*x^2/(1-2*x-4*x^2). (End)

a(n) = 5*A063727(n-1). - R. J. Mathar, Mar 08 2021

Extensions

More terms from Franklin T. Adams-Watters, Aug 06 2009