Search: id:A077413
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%I A077413
%S A077413 2,13,76,443,2582,15049,87712,511223,2979626,17366533,101219572,
%T A077413 589950899,3438485822,20040964033,116807298376,680802826223,
%U A077413 3968009658962,23127255127549,134795521106332,785645871510443
%N A077413 Bisection (odd part) of Chebyshev sequence with Diophantine property.
%C A077413 -8*a(n)^2 + b(n)^2 = 17, with the companion sequence b(n)= A077239(n).
%C A077413 The even part is A054488(n) with Diophantine companion A077240(n).
%H A077413 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A077413 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A077413 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A077413 a(n)= 6*a(n-1) - a(n-2), a(-1) := -1, a(0)=2.
%F A077413 a(n)= 2*S(n, 6)+S(n-1, 6), with S(n, x) := U(n, x/2), Chebyshev polynomials 
               of 2nd kind, A049310. S(n, 6)= A001109(n+1).
%F A077413 G.f.: (2+x)/(1-6*x+x^2).
%e A077413 8*a(1)^2 + 17 = 8*13^2+17 = 1369 = 37^2 = A077239(1)^2.
%Y A077413 Cf. A077241 (even and odd parts).
%Y A077413 Sequence in context: A154357 A161130 A007509 this_sequence A024199 A037523 
               A037732
%Y A077413 Adjacent sequences: A077410 A077411 A077412 this_sequence A077414 A077415 
               A077416
%K A077413 nonn,easy
%O A077413 0,1
%A A077413 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 
               2002

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