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%I #24 Sep 08 2022 08:45:11
%S 2,29,843,24476,710647,20633239,599074578,17393796001,505019158607,
%T 14662949395604,425730551631123,12360848946698171,358890350005878082,
%U 10420180999117162549,302544139324403592003,8784200221406821330636,255044350560122222180447,7405070366464951264563599
%N a(n) = Lucas(7*n).
%C a(n+1)/a(n) converges to (29+sqrt(845))/2 = 29.0344418537...
%C a(0)/a(1) = 2/29, a(1)/a(2) = 29/843, a(2)/a(3) = 843/24476, a(3)/a(4) = 24476/710647, etc.
%C Lim_{n->infinity} a(n)/a(n+1) = 0.0344418537... = 2/(29+sqrt(845)) = (sqrt(845)-29)/2.
%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 (29, 1).
%F a(n) = 29*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 29.
%F a(n) = ((29 + sqrt(845))/2)^n + ((29 - sqrt(845))/2)^n.
%F a(n)^2 = a(2n) - 2 for n = 1, 3, 5, ...;
%F a(n)^2 = a(2n) + 2 for n = 2, 4, 6, ....
%F G.f.: (2-29*x)/(1-29*x-x^2). - _Philippe Deléham_, Nov 02 2008
%e a(4) = 710647 = 29*a(3) + a(2) = 29*24476 + 843 = ((29+sqrt(845))/2)^4 + ((29-sqrt(845))/2)^4 = 710646.9999985928... + 0.0000014071... = 710647.
%t LucasL[7Range[0,20]] (* or *) LinearRecurrence[{29,1},{2,29},20] (* _Harvey P. Dale_, Nov 22 2011 *)
%o (Magma) [ Lucas(7*n) : n in [0..100]]; // _Vincenzo Librandi_, Apr 14 2011
%Y Cf. A000032.
%K easy,nonn
%O 0,1
%A Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003
%E More terms from _Ray Chandler_, Feb 14 2004
%E More terms from _Vincenzo Librandi_, Apr 14 2011
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