Search: id:A077235
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%I A077235
%S A077235 5,16,59,220,821,3064,11435,42676,159269,594400,2218331,8278924,
%T A077235 30897365,115310536,430344779,1606068580,5993929541,22369649584,
%U A077235 83484668795,311569025596,1162791433589,4339596708760
%N A077235 Bisection (odd part) of Chebyshev sequence with Diophantine property.
%C A077235 a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n)= A077234(n).
%C A077235 The even part is A077236(n) with Diophantine companion A054491(n).
%H A077235 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077235 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077235 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077235 a(n)= 2*T(n+1, 2)+T(n, 2), with T(n, x) Chebyshev's polynomials of the 
               first kind, A053120. T(n, 2)= A001075(n).
%F A077235 G.f.: (5-4*x)/(1-4*x+x^2).
%F A077235 a(n)=4*a(n-1)-a(n-2) with a(0)=5 and a(1)=16. [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Nov 16 2008]
%F A077235 a(n)=-sqrt(3)*[2-sqrt(3)]^n+sqrt(3)*[2+sqrt(3)]^n+(5/2)*[2-sqrt(3)]^n+(5/
               2)*[2+sqrt(3)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), 
               Nov 20 2008]
%e A077235 16 = a(1) = sqrt(3*A077234(1)^2 + 13) = sqrt(3*9^2 + 13)= sqrt(256) = 
               16.
%Y A077235 Cf. A077238 (even and odd parts).
%Y A077235 Sequence in context: A006217 A116914 A047103 this_sequence A098347 A034532 
               A092497
%Y A077235 Adjacent sequences: A077232 A077233 A077234 this_sequence A077236 A077237 
               A077238
%K A077235 nonn,easy
%O A077235 0,1
%A A077235 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 
               2002

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