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 A157461 #16 Jun 27 2021 03:29:02 %S A157461 1,27,701,18199,472473,12266099,318446101,8267332527,214632199601, %T A157461 5572169857099,144661784084973,3755634216352199,97501827841072201, %U A157461 2531291889651525027,65716087303098578501,1706086977990911515999,44292545340460600837473 %N A157461 Expansion of x*(x+1) / (x^2-26*x+1). %C A157461 This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A: %C A157461 A * c(n)+1 = a(n)^2, %C A157461 (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014. %C A157461 A157461 is the b(n) sequence for A=6. %C A157461 Numbers k such that 42*k^2 + 7 is a square. - _Klaus Purath_, Jun 12 2021 %H A157461 Colin Barker, <a href="/A157461/b157461.txt">Table of n, a(n) for n = 1..700</a> %H A157461 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (26,-1). %F A157461 G.f.: x*(x+1) / (x^2-26*x+1). %F A157461 a(1) = 1, a(2) = 27, a(n) = 26*a(n-1)-a(n-2) for n>2. %F A157461 a(n) = (13+2*sqrt(42))^(-n)*(-6-sqrt(42)+(-6+sqrt(42))*(13+2*sqrt(42))^(2*n))/12. - _Colin Barker_, Jul 25 2016 %F A157461 a(n+1) = (a(n)^2 - 28)/a(n-1), n > 1. - _Klaus Purath_, Jun 12 2021 %o A157461 (PARI) Vec(x*(x+1)/(x^2-26*x+1)+O(x^20)) \\ _Charles R Greathouse IV_, Sep 26 2012 %o A157461 (PARI) a(n) = round((13+2*sqrt(42))^(-n)*(-6-sqrt(42)+(-6+sqrt(42))*(13+2*sqrt(42))^(2*n))/12) \\ _Colin Barker_, Jul 25 2016 %Y A157461 6*A157874(n)+1 = A153111(n)^2. %Y A157461 7*A157874(n)+1 = A157461(n)^2. %K A157461 nonn,easy %O A157461 1,2 %A A157461 _Paul Weisenhorn_, Mar 01 2009 %E A157461 Edited by _Alois P. Heinz_, Sep 09 2011