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A077243 Bisection (odd part) of Chebyshev sequence with Diophantine property.

%I A077243 #20 Jan 01 2024 11:05:36
%S A077243 2,17,134,1055,8306,65393,514838,4053311,31911650,251239889,
%T A077243 1978007462,15572819807,122604550994,965263588145,7599504154166,
%U A077243 59830769645183,471046653007298,3708542454413201,29197292982298310
%N A077243 Bisection (odd part) of Chebyshev sequence with Diophantine property.
%C A077243 -5*a(n)^2 + 3* b(n)^2 = 7, with the companion sequence b(n)= A077244(n).
%C A077243 The even part is A077245(n) with Diophantine companion A077246(n).
%H A077243 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A077243 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A077243 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-1).
%F A077243 a(n)= 8*a(n-1) - a(n-2), a(-1)=-1, a(0)=2.
%F A077243 a(n)= 2*S(n, 8)+S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 8)= A001090(n+1).
%F A077243 G.f.: (2+x)/(1-8*x+x^2).
%e A077243 5*a(1)^2 + 7 = 5*17^2+7 = 1452 = 3*22^2 = 3*A077244(1)^2.
%t A077243 LinearRecurrence[{8,-1},{2,17},30] (* _Harvey P. Dale_, Oct 03 2015 *)
%K A077243 nonn,easy
%O A077243 0,1
%A A077243 _Wolfdieter Lang_, Nov 08 2002