

A090313


a(n) = 22a(n1) + a(n2), 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
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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(n1) + a(n2), starting with a(0) = 2 and a(1) = 22. a(n) = (11+sqrt(122))^n + (11sqrt(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.: (222x)/(122xx^2). [From Philippe Deléham, Nov 02 2008]


EXAMPLE

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



