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A090301 a(n) = 15a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 15. 5
2, 15, 227, 3420, 51527, 776325, 11696402, 176222355, 2655031727, 40001698260, 602680505627, 9080209282665, 136805819745602, 2061167505466695, 31054318401746027, 467875943531657100, 7049193471376602527 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (15+sqrt(229))/2 = 15.066372... Lim a(n)/a(n+1) as n approaches infinity = 0.066372... = 2/(15+sqrt(229)) = (sqrt(229)-15)/2. Lim a(n+1)/a(n) as n approaches infinity = 15.066372... = (15+sqrt(229))/2 = 2/(sqrt(229)-15).

Contribution from Johannes W. Meijer, Jun 12 2010: (Start)

For more information about this type of recurrence follow the Khovanova link and see A054413, A086902 and A178765.

(End)

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 (15, 1).

FORMULA

a(n) =15a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 15. a(n) = ((15+sqrt(229))/2)^n + ((15-sqrt(229))/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.: (2-15*x)/(1-15*x-x^2). [From Philippe Deléham, Nov 02 2008]

Contribution from Johannes W. Meijer, Jun 12 2010: (Start)

Limit(a(n+k)/a(k), k=infinity) = (A090301(n) + A154597(n)*sqrt(229))/2

Limit(A090301(n)/ A154597(n), n=infinity) = sqrt(229)

(End)

EXAMPLE

a(4) = 51527 = 15a(3) + a(2) = 15*3420+ 227=((15+sqrt(229))/2)^4 + ((15-sqrt(229))/2)^4 = 51526.9999805 + 0.0000194 =51527

CROSSREFS

Cf. A058087, A071416.

Contribution from Johannes W. Meijer, Jun 12 2010: (Start)

a(2n+1) = 15*A098246(n).

a(3n+1) = A041426(5n), a(3n+2) = A041426(5n+3), a(3n+3) = 2*A041426(5n+4).

(End)

Sequence in context: A176337 A145168 A184357 * A247660 A197236 A097628

Adjacent sequences:  A090298 A090299 A090300 * A090302 A090303 A090304

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.