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 A077245 #18 Jan 01 2024 11:05:40 %S A077245 1,10,79,622,4897,38554,303535,2389726,18814273,148124458,1166181391, %T A077245 9181326670,72284431969,569094129082,4480468600687,35274654676414, %U A077245 277716768810625,2186459495808586,17213959197658063 %N A077245 Bisection (even part) of Chebyshev sequence with Diophantine property. %C A077245 3*b(n)^2 - 5*a(n)^2 = 7, with the companion sequence b(n)= A077246(n). %C A077245 The odd part is A077243(n) with Diophantine companion A077244(n). %H A077245 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a> %H A077245 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A077245 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-1). %F A077245 a(n)= 8*a(n-1) - a(n-2), a(-1) := -2, a(0)=1. %F A077245 a(n)= S(n, 8)+2*S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x) := 0 and S(n, 8)= A001090(n+1). %F A077245 G.f.: (1+2*x)/(1-8*x+x^2). %e A077245 5*a(1)^2 + 7 = 5*10^2 + 7 = 507 = 3*13^2 = 3*A077246(1)^2. %K A077245 nonn,easy %O A077245 0,2 %A A077245 _Wolfdieter Lang_, Nov 08 2002