Search: id:A077240
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%I A077240
%S A077240 5,23,133,775,4517,26327,153445,894343,5212613,30381335,177075397,
%T A077240 1032071047,6015350885,35060034263,204344854693,1191009093895,
%U A077240 6941709708677,40459249158167,235813785240325,1374423462283783
%N A077240 Bisection (even part) of Chebyshev sequence with Diophantine property.
%C A077240 a(n)^2 - 8*b(n)^2 = 17, with the companion sequence b(n)= A054488(n).
%C A077240 The odd part is A077239(n) with Diophantine companion A077413(n).
%H A077240 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077240 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077240 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077240 a(n)= 6*a(n-1) - a(n-2), a(-1) := 7, a(0)=5.
%F A077240 a(n)= T(n+1, 3)+2*T(n, 3), with T(n, x) Chebyshev's polynomials of the 
               first kind, A053120. T(n, 3)= A001541(n).
%F A077240 G.f.: (5-7*x)/(1-6*x+x^2).
%e A077240 23 = a(1) = sqrt(8*A054488(1)^2 + 17) = sqrt(8*8^2 + 17)= sqrt(529) = 
               23.
%Y A077240 Cf. A077242 (even and odd parts).
%Y A077240 Sequence in context: A020032 A009321 A078509 this_sequence A129098 A047049 
               A020034
%Y A077240 Adjacent sequences: A077237 A077238 A077239 this_sequence A077241 A077242 
               A077243
%K A077240 nonn,easy
%O A077240 0,1
%A A077240 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 
               2002

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