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A090308 a(n) = 19a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 19. 1
2, 19, 363, 6916, 131767, 2510489, 47831058, 911300591, 17362542287, 330799604044, 6302555019123, 120079344967381, 2287810109399362, 43588471423555259, 830468767156949283, 15822495047405591636 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (19+sqrt(365))/2 = 19.052486... Lim a(n)/a(n+1) as n approaches infinity = 0.052486... = 2/(19+sqrt(365)) = (sqrt(365)-19)/2. Lim a(n+1)/a(n) as n approaches infinity = 19.052486... = (19+sqrt(365))/2 = 2/(sqrt(365)-19).

LINKS

Table of n, a(n) for n=0..15.

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

Index entries for linear recurrences with constant coefficients, signature (19, 1).

FORMULA

a(n) =19a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 19. a(n) = ((19+sqrt(365))/2)^n + ((19-sqrt(365))/2)^n, (a(n))^2 =a(2n)-2 if n=1, 3, 5..., (a(n))^2 =a(2n)+2 if n=2, 4, 6....

G.f.: (2-19x)/(1-19x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) = 131767 = 19a(3) + a(2) = 19*6916+ 363=((19+sqrt(365))/2)^4 + ((19-sqrt(365))/2)^4 = 131766.9999924108 + 0.0000075891 = 131767.

CROSSREFS

Cf. A049270.

Sequence in context: A233107 A187659 A078369 * A110818 A155927 A120420

Adjacent sequences:  A090305 A090306 A090307 * A090309 A090310 A090311

KEYWORD

easy,nonn

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004

EXTENSIONS

More terms from Ray Chandler, Feb 14 2004

STATUS

approved

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Last modified April 27 00:46 EDT 2017. Contains 285506 sequences.