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%I #28 Dec 07 2019 12:18:24
%S 2,20,398,7940,158402,3160100,63043598,1257711860,25091193602,
%T 500566160180,9986232009998,199224074039780,3974495248785602,
%U 79290680901672260,1581839122784659598,31557491774791519700,629567996373045734402,12559802435686123168340
%N a(n) = 20*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 20.
%C Except for the first term, positive values of x (or y) satisfying x^2 - 20xy + y^2 + 396 = 0. - _Colin Barker_, Feb 28 2014
%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 (20,-1).
%F a(n) = p^n + q^n, where p = 10 + 3*sqrt(11) and q = 10 - 3*sqrt(11). - _Tanya Khovanova_, Feb 06 2007
%F G.f.: (2-20*x)/(1-20*x+x^2). - _Philippe Deléham_, Nov 02 2008
%t a[0] = 2; a[1] = 20; a[n_] := 20a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* _Robert G. Wilson v_, Jan 30 2004 *)
%o (Sage) [lucas_number2(n,20,1) for n in range(0,20)] # _Zerinvary Lajos_, Jun 27 2008
%o (PARI) Vec((2-20*x)/(1-20*x+x^2) + O(x^100)) \\ _Colin Barker_, Feb 28 2014
%Y Cf. A080959, A037035, A054877.
%Y Cf. A001085.
%K easy,nonn
%O 0,1
%A Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 18 2004
%E More terms from _Robert G. Wilson v_, Jan 30 2004
%E More terms from _Colin Barker_, Feb 28 2014
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