Search: id:A057076
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%I A057076
%S A057076 2,11,119,1298,14159,154451,1684802,18378371,200477279,
%T A057076 2186871698,23855111399,260219353691,2838557779202,30963916217531,
%U A057076 337764520613639,3684445810532498,40191139395243839,438418087537149731
%N A057076 A Chebyshev or generalized Fibonacci sequence.
%H A057076 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A057076 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A057076 <a href="Sindx_Rea.html#recur1">Index entries for recurrences a(n) = 
               k*a(n - 1) +/- a(n - 2)</a>
%H A057076 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A057076 a(n) = S(n, 11) - S(n-2, 11) = 2*T(n, 11/2) with S(n, x) := U(n, x/2), 
               S(-1, x) := 0, S(-2, x) := -1. S(n, 11)=A004190(n). U-, resp. T-, 
               are Chebyshev's polynomials of the second, resp. first, case. See 
               A049310 and A053120.
%F A057076 G.f.: (2-11x)/(1-11x+x^2).
%F A057076 a(n)=a(-n). - Michael Somos, Apr 25 2003
%F A057076 a(n) = ap^n + am^n, with ap := (11+sqrt(117))/2 and am := (11-sqrt(117))/
               2.
%t A057076 a[0] = 2; a[1] = 11; a[n_] := 11a[n - 1] - a[n - 2]; Table[ a[n], {n, 
               0, 17}] (from Robert G. Wilson v Jan 30 2004)
%o A057076 (PARI) a(n)=subst(poltchebi(n),x,11/2)*2
%o A057076 sage: [lucas_number2(n,11,1) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 25 2008
%Y A057076 a(n)=sqrt(4+117*A004190(n-1)^2), n>=1.
%Y A057076 Sequence in context: A069574 A090534 A130222 this_sequence A118794 A155928 
               A001946
%Y A057076 Adjacent sequences: A057073 A057074 A057075 this_sequence A057077 A057078 
               A057079
%K A057076 nonn,easy
%O A057076 0,1
%A A057076 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 31 
               2002

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