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A090307 a(n) = 18a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 18. 1
2, 18, 326, 5886, 106274, 1918818, 34644998, 625528782, 11294163074, 203920464114, 3681862517126, 66477445772382, 1200275886420002, 21671443401332418, 391286257110403526, 7064824071388595886 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (9+sqrt(82)) = 18.0553851... Lim a(n)/a(n+1) as n approaches infinity = 0.0553851... = 1/(9+sqrt(82)) = (sqrt(82)-9). Lim a(n+1)/a(n) as n approaches infinity = 18.0553851... = (9+sqrt(82)) = 1/(sqrt(82)-9).

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 (18, 1).

FORMULA

a(n) =18a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 18. a(n) = (9+sqrt(82))^n + (9-sqrt(82))^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.: (2-18x)/(1-18x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) =106274 = 18a(3) + a(2) = 18*5886+ 326 = (9+sqrt(82))^4 + (9-sqrt(82))^4 =106273.9999905903 + 0.000009406 = 106274.

MATHEMATICA

LinearRecurrence[{18, 1}, {2, 18}, 25] (* or *) CoefficientList[ Series[ (2-18x)/(1-18x-x^2), {x, 0, 25}], x] (* Harvey P. Dale, Apr 22 2011 *)

CROSSREFS

Cf. A083218, A087215.

Sequence in context: A192985 A193264 A191492 * A123311 A181536 A132911

Adjacent sequences:  A090304 A090305 A090306 * A090308 A090309 A090310

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 29 01:04 EDT 2017. Contains 285604 sequences.