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A090306 a(n) = 17a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 17. 5
2, 17, 291, 4964, 84679, 1444507, 24641298, 420346573, 7170533039, 122319408236, 2086600473051, 35594527450103, 607193567124802, 10357885168571737, 176691241432844331, 3014108989526925364, 51416544063390575519 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (17+sqrt(293))/2 = 17.058621... Lim a(n)/a(n+1) as n approaches infinity = 0.058621... = 2/(17+sqrt(293)) = (sqrt(293)-17)/2. Lim a(n+1)/a(n) as n approaches infinity = 17.058621... = (17+sqrt(293))/2 = 2/(sqrt(293)-17).

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 (17, 1).

FORMULA

a(n) =17a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 17. a(n) = ((17+sqrt(293))/2)^n + ((17-sqrt(293))/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.: (2-17x)/(1-17x-x^2). [From Philippe Deléham, Nov 02 2008]

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

a(2n+1) = 17*A098249(n).

a(3n+1) = A041550(5n), a(3n+2) = A041550(5n+3), a(3n+3) = 2*A041550(5n+4).

Limit(a(n+k)/a(k), k=infinity) = (A090306(n) + A178765(n)*sqrt(293))/2

Limit(A090306(n)/A178765(n), n=infinity) = sqrt(293)

(End)

EXAMPLE

a(4) = 84679 = 17a(3) + a(2) = 17*4964+ 291=((17+sqrt(293))/2)^4 + ((17-sqrt(293))/2)^4 = 84678.999988190 + 0.000011809 =84679.

CROSSREFS

Cf. A005074.

Sequence in context: A198287 A268705 A078367 * A007785 A201785 A204249

Adjacent sequences:  A090303 A090304 A090305 * A090307 A090308 A090309

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 August 18 10:57 EDT 2017. Contains 290712 sequences.