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A090316 a(n) = 24a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 24. 1
2, 24, 578, 13896, 334082, 8031864, 193098818, 4642403496, 111610782722, 2683301188824, 64510839314498, 1550943444736776, 37287153512997122, 896442627756667704, 21551910219673022018, 518142287899909196136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (12+sqrt(145)) = 24.0415945... Lim a(n)/a(n+1) as n approaches infinity = 0.0415945... = 1/(12+sqrt(145)) = (sqrt(145)-12). Lim a(n+1)/a(n) as n approaches infinity = 24.0415945... = (12+sqrt(145)) = 1/(sqrt(145)-12).

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 (24,1).

FORMULA

a(n) =24a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 24. a(n) = (12+sqrt(145))^n + (12-sqrt(145))^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.: (2-24x)/(1-24x-x^2). [From Philippe Deléham, Nov 02 2008]

EXAMPLE

a(4) =334082 = 24a(3) + a(2) = 24*13896+ 578 = (12+sqrt(145))^4 + (12-sqrt(145))^4 = 334081.99999700672 + 0.00000299327 = 334082.

MATHEMATICA

LinearRecurrence[{24, 1}, {2, 24}, 20] (* Harvey P. Dale, Aug 30 2015 *)

CROSSREFS

Cf. A058168, A056949.

Sequence in context: A090732 A014298 A280794 * A128578 A186632 A089835

Adjacent sequences:  A090313 A090314 A090315 * A090317 A090318 A090319

KEYWORD

easy,nonn

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004

EXTENSIONS

More terms from Ray Chandler, Feb 14 2004

Corrected by T. D. Noe, Nov 07 2006

STATUS

approved

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Last modified June 24 20:19 EDT 2017. Contains 288707 sequences.