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A090309 a(n) = 20a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 20. 2
2, 20, 402, 8060, 161602, 3240100, 64963602, 1302512140, 26115206402, 523606640180, 10498248010002, 210488566840220, 4220269584814402, 84615880263128260, 1696537874847379602, 34015373377210720300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (10+sqrt(101)) = 20.0498756... Lim a(n)/a(n+1) as n approaches infinity = 0.0498756... = 1/(10+sqrt(101)) = (sqrt(101)-10). Lim a(n+1)/a(n) as n approaches infinity = 20.0498756... = (10+sqrt(101)) = 1/(sqrt(101)-10).

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 (20, 1).

FORMULA

a(n) =20a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 20. a(n) = (10+sqrt(101))^n + (10-sqrt(101))^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.: (2-20*x)/(1-20*x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) =161602 = 20a(3) + a(2) = 20*8060+ 402 = (10+sqrt(101))^4 + (10-sqrt(101))^4 =161601.999993811 + 0.000006188 = 161602.

MATHEMATICA

LinearRecurrence[{20, 1}, {2, 20}, 20] (* Harvey P. Dale, Nov 19 2015 *)

CROSSREFS

Cf. A002116.

Sequence in context: A078698 A090728 A210896 * A002116 A058346 A165554

Adjacent sequences:  A090306 A090307 A090308 * A090310 A090311 A090312

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 July 27 21:01 EDT 2017. Contains 289866 sequences.