Search: id:A077239
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%I A077239
%S A077239 7,37,215,1253,7303,42565,248087,1445957,8427655,49119973,286292183,
%T A077239 1668633125,9725506567,56684406277,330380931095,1925601180293,
%U A077239 11223226150663,65413755723685,381259308191447,2222142093424997
%N A077239 Bisection (odd part) of Chebyshev sequence with Diophantine property.
%C A077239 a(n)^2 - 8*b(n)^2 = 17, with the companion sequence b(n)= A077413(n).
%C A077239 The even part is A077240(n) with Diophantine companion A054488(n).
%H A077239 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077239 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077239 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077239 a(n)= 6*a(n-1) - a(n-2), a(-1) := 5, a(0)=7.
%F A077239 a(n)= 2*T(n+1, 3)+T(n, 3), with T(n, x) Chebyshev's polynomials of the 
               first kind, A053120. T(n, 3)= A001541(n).
%F A077239 G.f.: (7-5*x)/(1-6*x+x^2).
%e A077239 37 = a(1) = sqrt(8*A077413(1)^2 +17) = sqrt(8*13^2 + 17)= sqrt(1369) 
               = 37.
%Y A077239 Cf. A077242 (even and odd parts).
%Y A077239 Sequence in context: A124610 A002683 A126475 this_sequence A046235 A144496 
               A025012
%Y A077239 Adjacent sequences: A077236 A077237 A077238 this_sequence A077240 A077241 
               A077242
%K A077239 nonn,easy
%O A077239 0,1
%A A077239 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 
               2002

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