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%I #27 Mar 28 2020 13:10:11
%S 2,26,674,17498,454274,11793626,306180002,7948886426,206364867074,
%T 5357537657498,139089614227874,3610972432267226,93746193624720002,
%U 2433790061810452826,63184795413447053474,1640370890687812937498
%N a(n) = 26*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 26.
%C 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).
%H Indranil Ghosh, <a href="/A090247/b090247.txt">Table of n, a(n) for n = 0..705</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rea#recur1">Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (26,-1).
%F 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.
%F G.f.: (2-26*x)/(1-26*x+x^2). - _Philippe Deléham_, Nov 02 2008
%F a(n) = 2*A097308(n). - _R. J. Mathar_, Sep 27 2014
%e a(4) = 454274 = 26*a(3) - a(2) = 26*17498 - 674 = (13+sqrt(168))^4 + (13-sqrt(168))^4 = 454273.9999977986 + 0.0000022013 = 454274.
%t 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 *)
%o (Sage) [lucas_number2(n,26,1) for n in range(0,16)] # _Zerinvary Lajos_, Jun 27 2008
%Y Cf. A032000, A019586, A097308.
%K easy,nonn
%O 0,1
%A Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 24 2004
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