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 A077235 #23 Dec 31 2023 11:27:08 %S A077235 5,16,59,220,821,3064,11435,42676,159269,594400,2218331,8278924, %T A077235 30897365,115310536,430344779,1606068580,5993929541,22369649584, %U A077235 83484668795,311569025596,1162791433589,4339596708760,16195595401451,60442784897044,225575544186725 %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 Colin Barker, <a href="/A077235/b077235.txt">Table of n, a(n) for n = 0..1000</a> %H A077235 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a> %H A077235 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A077235 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1) %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. - _Philippe Deléham_, Nov 16 2008 %e A077235 16 = a(1) = sqrt(3*A077234(1)^2 + 13) = sqrt(3*9^2 + 13)= sqrt(256) = 16. %o A077235 (PARI) Vec((5-4*x)/(1-4*x+x^2) + O(x^100)) \\ _Colin Barker_, Jun 16 2015 %Y A077235 Cf. A077238 (even and odd parts). %K A077235 nonn,easy %O A077235 0,1 %A A077235 _Wolfdieter Lang_, Nov 08 2002