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%I #20 Jul 12 2020 17:10:33
%S 2,14,198,2786,39202,551614,7761798,109216786,1536796802,21624372014,
%T 304278004998,4281516441986,60245508192802,847718631141214,
%U 11928306344169798,167844007449518386,2361744410637427202
%N a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
%C a(n+1)/a(n) converges to (7+sqrt(50)) = 14.071067811...
%C Lim_{n->infinity} a(n)/a(n+1) = 0.071067811... = 1/(7+sqrt(50)) = sqrt(50) - 7.
%C Lim_{n->infinity} a(n+1)/a(n) = 14.071067811... = (7+sqrt(50)) = 1/(sqrt(50) - 7).
%H Harvey P. Dale, <a href="/A090300/b090300.txt">Table of n, a(n) for n = 0..870</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 (14, 1).
%F a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
%F a(n) = (7+sqrt(50))^n + (7-sqrt(50))^n.
%F (a(n))^2 = a(2n)-2 if n = 1, 3, 5, ...; (a(n))^2 = a(2n)+2 if n = 2, 4, 6, ....
%F G.f.: (2-14*x)/(1-14*x-x^2). - _Philippe Deléham_, Nov 02 2008
%e a(4) = 39202 = 14*a(3) + a(2) = 14*2786 + 198 = (7+sqrt(50))^4 + (7-sqrt(50))^4 = 39201.999974491 + 0.000025508 = 39202.
%t LinearRecurrence[{14,1},{2,14},20] (* _Harvey P. Dale_, Jul 12 2020 *)
%Y Cf. A050012.
%K easy,nonn
%O 0,1
%A Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004
%E More terms from _Ray Chandler_, Feb 14 2004
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