Search: id:A077234
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%I A077234
%S A077234 2,9,34,127,474,1769,6602,24639,91954,343177,1280754,4779839,17838602,
%T A077234 66574569,248459674,927264127,3460596834,12915123209,48199896002,
%U A077234 179884460799,671337947194,2505467327977,9350531364714,34896658130879
%N A077234 Bisection (odd part) of Chebyshev sequence with Diophantine property.
%C A077234 -3*a(n)^2 + b(n)^2 = 13, with the companion sequence b(n)= A077235(n).
%C A077234 The even part is A054491(n) with Diophantine companion A077236(n).
%H A077234 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077234 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077234 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077234 a(n)= 2*S(n, 4)+S(n-1, 4), with S(n, x) := U(n, x/2), Chebyshev polynomials 
               of 2nd kind, A049310. S(-1, x) := 0 and S(n, 4)= A001353(n+1).
%F A077234 G.f.: (2+x)/(1-4*x+x^2).
%F A077234 a(n)=4*a(n-1)-a(n-2) with a(0)=2 and a(1)=9. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 16 2008]
%F A077234 a(n)=-(5/6)*sqrt(3)*[2-sqrt(3)]^n+(5/6)*sqrt(3)*[2+sqrt(3)]^n+[2-sqrt(3)]^n+[2+sqrt(3)]^n, 
               with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 20 2008]
%e A077234 3*a(1)^2 + 13 = 3*81+13 = 256 = 16^2 = A077235(1)^2.
%Y A077234 Cf. A077237 (even and odd parts).
%Y A077234 Sequence in context: A000524 A120989 A010763 this_sequence A091526 A150937 
               A150938
%Y A077234 Adjacent sequences: A077231 A077232 A077233 this_sequence A077235 A077236 
               A077237
%K A077234 nonn,easy
%O A077234 0,1
%A A077234 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 
               2002

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