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A090313 a(n) = 22a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 22. 1
2, 22, 486, 10714, 236194, 5206982, 114789798, 2530582538, 55787605634, 1229857906486, 27112661548326, 597708411969658, 13176697724880802, 290485058359347302, 6403847981630521446, 141175140654230819114 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (11+sqrt(122)) = 22.045361... Lim a(n)/a(n+1) as n approaches infinity = 0.045361... = 1/(11+sqrt(122)) = (sqrt(122)-11). Lim a(n+1)/a(n) as n approaches infinity = 22.045361... = (11+sqrt(122)) = 1/(sqrt(122)-11).

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 (22, 1).

FORMULA

a(n) =22a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 22. a(n) = (11+sqrt(122))^n + (11-sqrt(122))^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.: (2-22x)/(1-22x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) =236194 = 22a(3) + a(2) = 22*10714+ 486 = (11+sqrt(122))^4 + (11-sqrt(122))^4 = 236193.999995766 + 0.000004233 = 236194.

CROSSREFS

Cf. A079219.

Sequence in context: A276454 A137076 A090730 * A110129 A246740 A248798

Adjacent sequences:  A090310 A090311 A090312 * A090314 A090315 A090316

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 23 02:45 EDT 2017. Contains 288633 sequences.