Search: id:A077420
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%I A077420
%S A077420 1,33,1121,38081,1293633,43945441,1492851361,50713000833,1722749176961,
%T A077420 58522759015841,1988051057361633,67535213191279681,2294209197446147521,
%U A077420 77935577499977736033,2647515425801796877601
%N A077420 Bisection of Chebyshev sequence T(n,3) (odd part) with Diophantine property.
%C A077420 (3*a(n))^2 - 2*(2*b(n))^2 = 1 with companion sequence b(n)= A046176(n+1), 
               n>=0 (special solutions of Pell equation).
%H A077420 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077420 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077420 a(n) = 34*a(n-1) - a(n-2), a(-1)=1, a(0)=1.
%F A077420 a(n) = T(2*n+1, 3)/3 = S(n, 34) - S(n-1, 34) with S(n, x) := U(n, x/2), 
               resp. T(n, x), Chebyshev's polynomials of the second, resp. first, 
               kind. See A049310 and A053120. S(-1, x)=0, S(n, 34)= A029547(n), 
               T(n, 3)=A001541(n).
%F A077420 G.f.: (1-x)/(1-34*x+x^2).
%F A077420 a(n)= sqrt(8*A046176(n+1)^2 + 1)/3.
%Y A077420 Cf. A056771 (even part).
%Y A077420 Row 34 of array A094954.
%Y A077420 Sequence in context: A132469 A009977 A130835 this_sequence A158688 A065424 
               A071268
%Y A077420 Adjacent sequences: A077417 A077418 A077419 this_sequence A077421 A077422 
               A077423
%K A077420 nonn,easy
%O A077420 0,2
%A A077420 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 
               2002

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