Search: id:A097725
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%I A097725
%S A097725 1,102,10403,1061004,108212005,11036563506,1125621265607,
%T A097725 114802332528408,11708712296632009,1194173851923936510,
%U A097725 121794024183944892011,12421796292910455048612
%N A097725 Chebyshev U(n,x) polynomial evaluated at x=51.
%C A097725 Used to form integer solutions of Pell equation a^2 - 26*b^2 =-1. See 
               A097726 with A097727.
%H A097725 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A097725 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A097725 a(n) = 102*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F A097725 a(n) = S(n, 2*51)= U(n, 51), Chebyshev's polynomials of the second kind. 
               See A049310.
%F A097725 G.f.: 1/(1-102*x+x^2).
%F A097725 a(n)= sum((-1)^k*binomial(n-k, k)*102^(n-2*k), k=0..floor(n/2)), n>=0.
%F A097725 a(n) = ((51+10*sqrt(26))^(n+1) - (51-10*sqrt(26))^(n+1))/(20*sqrt(26)).
%Y A097725 Sequence in context: A088805 A163435 A030512 this_sequence A129751 A094095 
               A074675
%Y A097725 Adjacent sequences: A097722 A097723 A097724 this_sequence A097726 A097727 
               A097728
%K A097725 nonn,easy
%O A097725 0,2
%A A097725 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Aug 31 2004

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