Search: id:A086903
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%I A086903
%S A086903 2,8,62,488,3842,30248,238142,1874888,14760962,116212808,914941502,
%T A086903 7203319208,56711612162,446489578088,3515205012542,27675150522248,
%U A086903 217885999165442,1715412842801288,13505416743244862,106327921103157608
%N A086903 a(n) = 8a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 8, a(n) = 
               (4+sqrt(15))^n + (4-sqrt(15))^n.
%C A086903 a(n+1)/a(n) converges to (4+sqrt(15)) = 7.872983... a(0)/a(1)=2/8; a(1)/
               a(2)=8/62; a(2)/a(3)=62/488; a(3)/a(4)=488/3842; ... etc. Lim a(n)/
               a(n+1) as n approaches infinity = 0.127016... = 1/(4+sqrt(15)) = 
               (4-sqrt(15)).
%C A086903 Twice A001091. - John W. Layman (layman(AT)math.vt.edu), Sep 25 2003
%H A086903 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A086903 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A086903 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%F A086903 G.f.: (2-8*x)/(1-8*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 02 2008]
%e A086903 a(4) = 3842 = 8a(3) - a(2) = 8*488 - 62 = (4+sqrt(15))^4 + (4-sqrt(15))^4 
               =
%e A086903 3841.9997397 + 0.0002603 = 3842.
%t A086903 a[0] = 2; a[1] = 8; a[n_] := 8a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 
               19}] (from Robert G. Wilson v Jan 30 2004)
%o A086903 sage: [lucas_number2(n,8,1) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 25 2008
%Y A086903 Cf. A086594, A058316, A006245, A009271.
%Y A086903 Sequence in context: A140722 A116976 A132574 this_sequence A161566 A159476 
               A006245
%Y A086903 Adjacent sequences: A086900 A086901 A086902 this_sequence A086904 A086905 
               A086906
%K A086903 easy,nonn
%O A086903 0,1
%A A086903 Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003

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