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

1,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000032, A000079, A084057, A000045.

Sequence in context: A179306 A117865 A249059 * A001692 A038070 A364738

Adjacent sequences: A163302 A163303 A163304 * A163306 A163307 A163308

Keyword

nonn,easy

Author

Mark Dols, Jul 24 2009

Extensions

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

Status

approved