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A087287 Lucas numbers L(9*n). 2
2, 76, 5778, 439204, 33385282, 2537720636, 192900153618, 14662949395604, 1114577054219522, 84722519070079276, 6440026026380244498, 489526700523968661124, 37210469265847998489922, 2828485190904971853895196, 215002084978043708894524818, 16342986943522226847837781364, 1242282009792667284144565908482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (76+sqrt(5780))/2 = 76.01315561749... a(0)/a(1)=2/76; a(1)/a(2)=76/5778; a(2)/a(3)= 5778/439204; a(3)/a(4)= 439204/33385282; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.01315561749... = 2/(76+sqrt(5780)) = (sqrt(5780)-76)/2.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..530

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 (76, 1).

FORMULA

a(n) = 76a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 76.

a(n) = ((76+sqrt(5780))/2)^n + ((76-sqrt(5780))/2)^n.

(a(n))^2 =a(2n)-2 for n=1, 3, 5..., (a(n))^2 =a(2n)+2 for n=2, 4, 6....

G.f.: (2-76*x)/(1-76*x-x^2). - Philippe Deléham, Nov 02 2008

EXAMPLE

a(4) = 33385282 = 76*a(3) + a(2) = 76*439204+ 5778=((76+sqrt(5780))/2)^4 + ( (76-sqrt(5780))/2)^4 =33385281.999999970046 + 0.000000029953 =33385282.

PROG

(MAGMA) [ Lucas(9*n) : n in [0..100]]; // Vincenzo Librandi, Apr 14 2011

(PARI) a(n)=fibonacci(9*n-1)+fibonacci(9*n+1) \\ Charles R Greathouse IV, Feb 06 2017

CROSSREFS

Cf. A000032.

Sequence in context: A198651 A198658 A277298 * A266877 A041721 A048358

Adjacent sequences:  A087284 A087285 A087286 * A087288 A087289 A087290

KEYWORD

easy,nonn

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003

EXTENSIONS

More terms from Vincenzo Librandi, Apr 14 2011

STATUS

approved

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Last modified August 23 01:14 EDT 2017. Contains 290953 sequences.