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A090247 a(n) = 26*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 26. 1
2, 26, 674, 17498, 454274, 11793626, 306180002, 7948886426, 206364867074, 5357537657498, 139089614227874, 3610972432267226, 93746193624720002, 2433790061810452826, 63184795413447053474, 1640370890687812937498 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n+1)/a(n) converges to (13+sqrt(168)) =25.9614813... Lim a(n)/a(n+1) as n approaches infinity = 0.0385186... = 1/(13+sqrt(168)) = (13-sqrt(168)). Lim a(n+1)/a(n) as n approaches infinity = 25.9614813... = (13+sqrt(168)) = 1/(13-sqrt(168)). Lim a(n)/a(n+1) = 26 - Lim a(n+1)/a(n).

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..705

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 (26,-1).

FORMULA

a(n) =26a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 26. a(n) = (13+sqrt(168))^n + (13-sqrt(168))^n. (a(n))^2 =a(2n)+2.

G.f.: (2-26*x)/(1-26*x+x^2). - Philippe Deléham, Nov 02 2008

EXAMPLE

a(4) = 454274 = 26a(3) - a(2) = 26*17498 - 674 =(13+sqrt(168))^4 + (13-sqrt(168))^4 =454273.9999977986 + 0.0000022013 =454274.

a(n) = 2*A097308(n). - R. J. Mathar, Sep 27 2014

MATHEMATICA

a[0] = 2; a[1] = 26; a[n_] := 26a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)

PROG

(Sage) [lucas_number2(n, 26, 1) for n in xrange(0, 16)] # Zerinvary Lajos, Jun 27 2008

CROSSREFS

Cf. A032000, A019586.

Sequence in context: A216254 A177316 A255538 * A206601 A156211 A156212

Adjacent sequences:  A090244 A090245 A090246 * A090248 A090249 A090250

KEYWORD

easy,nonn

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 24 2004

STATUS

approved

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Last modified November 21 07:11 EST 2017. Contains 294995 sequences.