This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A077250 #22 Jun 19 2015 11:19:41 %S A077250 11,103,1019,10087,99851,988423,9784379,96855367,958769291,9490837543, %T A077250 93949606139,930005223847,9206102632331,91131021099463, %U A077250 902104108362299,8929910062523527,88396996516872971,875040055106206183,8662003554545188859,85744995490345682407 %N A077250 Bisection (odd part) of Chebyshev sequence with Diophantine property. %C A077250 a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n) = A077249(n). %C A077250 The even part is A077409(n) with Diophantine companion A077251(n). %H A077250 Colin Barker, <a href="/A077250/b077250.txt">Table of n, a(n) for n = 0..1000</a> %H A077250 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a> %H A077250 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A077250 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-1). %F A077250 a(n) = 10*a(n-1)- a(n-2), a(-1)=7, a(0)=11. %F A077250 a(n) = 2*T(n+1, 5)+T(n, 5), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 5)= A001079(n). %F A077250 a(n) = sqrt(25 + 24*A077249(n)^2). %F A077250 G.f.: (11-7*x)/(1-10*x+x^2). %e A077250 103 = a(1) = sqrt(24*A077249(1)^2 + 25) = sqrt(24*21^2 + 25) = sqrt(10609) = 103. %t A077250 CoefficientList[Series[(11 - 7 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 11 2011 *) %o A077250 (PARI) a(n)= 2*polchebyshev(n+1,1,5)+polchebyshev(n,1,5) \\ _Charles R Greathouse IV_, Jun 11 2011 %o A077250 (PARI) Vec((11-7*x)/(1-10*x+x^2) + O(x^30)) \\ _Colin Barker_, Jun 15 2015 %K A077250 nonn,easy %O A077250 0,1 %A A077250 _Wolfdieter Lang_, Nov 08 2002