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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

(list; graph; refs; listen; history; text; internal format)

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)