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A090314 a(n) = 23a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 23. 1
2, 23, 531, 12236, 281959, 6497293, 149719698, 3450050347, 79500877679, 1831970236964, 42214816327851, 972772745777537, 22415987969211202, 516540496037635183, 11902847396834820411, 274282030623238504636 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (23+sqrt(533))/2 =23.04339638... Lim a(n)/a(n+1) as n approaches infinity = 0.04339638... = 2/(23+sqrt(533)) = (sqrt(533)-23)/2. Lim a(n+1)/a(n) as n approaches infinity = 23.04339638... = (23+sqrt(533))/2 = 2/(sqrt(533)-23).

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 (23, 1).

FORMULA

a(n) =23a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 23. a(n) = ((23+sqrt(533))/2)^n + ((23-sqrt(533))/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.: (2-23x)/(1-23x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4)=281959= 23a(3) + a(2) = 23*12236+ 531=((23+sqrt(533))/2)^4 + ((23-sqrt(533))/2)^4 = 281958.999996453 + 0.000003546 = 281959.

MATHEMATICA

LinearRecurrence[{23, 1}, {2, 23}, 20] (* Harvey P. Dale, Jul 11 2014 *)

CROSSREFS

Cf. A089141, A051502.

Sequence in context: A167417 A053161 A090731 * A084322 A073062 A015098

Adjacent sequences:  A090311 A090312 A090313 * A090315 A090316 A090317

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 July 20 16:53 EDT 2017. Contains 289628 sequences.