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A090300 a(n) = 14a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14. 1
2, 14, 198, 2786, 39202, 551614, 7761798, 109216786, 1536796802, 21624372014, 304278004998, 4281516441986, 60245508192802, 847718631141214, 11928306344169798, 167844007449518386, 2361744410637427202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (7+sqrt(50)) = 14.071067811... Lim a(n)/a(n+1) as n approaches infinity = 0.071067811... = 1/(7+sqrt(50)) = (sqrt(50)-7). Lim a(n+1)/a(n) as n approaches infinity = 14.071067811... = (7+sqrt(50)) = 1/(sqrt(50)-7).

LINKS

Table of n, a(n) for n=0..16.

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 (14, 1).

FORMULA

a(n) =14a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14. a(n) = (7+sqrt(50))^n + (7-sqrt(50))^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.: (2-14*x)/(1-14*x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) = 39202 = 14a(3) + a(2) = 14*2786+ 198 = (7+sqrt(50))^4 + (7-sqrt(50))^4 =39201.999974491 + 0.000025508 = 39202.

CROSSREFS

Cf. A050012.

Sequence in context: A232686 A263766 A244577 * A213977 A102224 A123543

Adjacent sequences:  A090297 A090298 A090299 * A090301 A090302 A090303

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 June 27 21:39 EDT 2017. Contains 288804 sequences.