Search: id:A086902
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%I A086902
%S A086902 2,7,51,364,2599,18557,132498,946043,6754799,48229636,344362251,
%T A086902 2458765393,17555720002,125348805407,894997357851,6390330310364,
%U A086902 45627309530399,325781497023157,2326097788692498,16608466017870643
%N A086902 a(n) = 7a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 7, a(n) = 
               [(7+sqrt(53))/2]^n + [(7-sqrt(53))/2]^n.
%C A086902 a(n+1)/a(n) converges to (7+sqrt(53))/2 = 7.14005... a(0)/a(1)=2/7; a(1)/
               a(2)=7/51; a(2)/a(3)=51/364; a(3)/a(4)=364/2599; ... etc. Lim a(n)/
               a(n+1) as n approaches infinity = 0.1400549... = 2/(7+sqrt(53)) = 
               (sqrt(53)-7)/2.
%H A086902 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A086902 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A086902 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%H A086902 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A086902 a(n) = 7a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 7, a(n) = 
               [(7+sqrt(53))/2]^n + [(7-sqrt(53))/2]^n.
%F A086902 E.g.f. : 2exp(7x/2)cosh(sqrt(53)x/2); a(n)=2^(1-n)sum{k=0..floor(n/2), 
               C(n, 2k)53^k7^(n-2k)}. a(n)=2T(n, 7i/2)(-i)^n with T(n, x) Chebyshev's 
               polynomials of the first kind (see A053120) and i^2=-1. - Paul Barry 
               (pbarry(AT)wit.ie), Nov 15 2003
%F A086902 G.f.: (2-7x)/(1-7x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 16 2008]
%e A086902 a(4) = 2599 = 7a(3) + a(2) = 7*364 + 51 = [(7+sqrt(53))/2]^4 + [(7-sqrt(53))/
               2]^4 =
%e A086902 2598.999615 + 0.000385 = 2599
%Y A086902 Cf. A058316.
%Y A086902 Sequence in context: A045598 A139008 A058721 this_sequence A138737 A046662 
               A118191
%Y A086902 Adjacent sequences: A086899 A086900 A086901 this_sequence A086903 A086904 
               A086905
%K A086902 easy,nonn
%O A086902 0,1
%A A086902 Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 18 2003
%E A086902 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 
               2004

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