Search: id:A097739
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%I A097739
%S A097739 1,325,105949,34539049,11259624025,3670602893101,1196605283526901,
%T A097739 390089651826876625,127168029890278252849,41456387654578883552149,
%U A097739 13514655207362825759747725,4405736141212626618794206201
%N A097739 Pell equation solutions (9*b(n))^2 - 82*a(n)^2 = -1 with b(n):=A097738(n), 
               n>=0.
%H A097739 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A097739 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A097739 a(n)= S(n, 2*163) - S(n-1, 2*163) = T(2*n+1, sqrt(82))/sqrt(82), with 
               Chebyshev polynomials of the 2nd and first kind. See A049310 for 
               the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: 
               U(-1, x); and A053120 for the T-triangle.
%F A097739 a(n)= ((-1)^n)*S(2*n, 18*I) with the imaginary unit I and Chebyshev polynomials 
               S(n, x) with coefficients shown in A049310.
%F A097739 G.f.: (1-x)/(1- 326*x+x^2).
%F A097739 a(n)=326*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=325 . [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Nov 18 2008]
%e A097739 (x,y) = (9*1=9;1), (2943=9*327;325), (959409=9*106601;105949), ... give 
               the positive integer solutions to x^2 - 82*y^2 =-1.
%Y A097739 Cf. A097737 for S(n, 326).
%Y A097739 Sequence in context: A166220 A121000 A048909 this_sequence A048918 A031516 
               A066128
%Y A097739 Adjacent sequences: A097736 A097737 A097738 this_sequence A097740 A097741 
               A097742
%K A097739 nonn,easy
%O A097739 0,2
%A A097739 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Aug 31 2004

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