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 A041126 #28 Jul 14 2015 16:53:14 %S A041126 8,17,280,577,9512,19601,323128,665857,10976840,22619537,372889432, %T A041126 768398401,12667263848,26102926097,430314081400,886731088897, %U A041126 14618011503752,30122754096401,496582077046168,1023286908188737,16869172608065960,34761632124320657 %N A041126 Numerators of continued fraction convergents to sqrt(72). %H A041126 Vincenzo Librandi, <a href="/A041126/b041126.txt">Table of n, a(n) for n = 0..100</a> %H A041126 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,34,0,-1). %F A041126 G.f.: -(x+1)*(x^2-9*x-8) / ((x^2-6*x+1)*(x^2+6*x+1)). - _Colin Barker_, Nov 05 2013 %F A041126 From _Gerry Martens_, Jul 11 2015: (Start) %F A041126 Interspersion of 2 sequences [a1(n),a0(n)] for n>0: %F A041126 a0(n) = (-4+3*sqrt(2))*(17+12*sqrt(2))^n-((4+3*sqrt(2))/(17+12*sqrt(2))^n). %F A041126 a1(n) = (1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/2. (End) %t A041126 Numerator[Convergents[Sqrt[72], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *) %t A041126 a0[n_] := (-4+3*Sqrt[2])*(17+12*Sqrt[2])^n-((4+3*Sqrt[2])/(17+12*Sqrt[2])^n) // Simplify %t A041126 a1[n_] := (1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/2 // FullSimplify %t A041126 Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* _Gerry Martens_, Jul 11 2015 *) %Y A041126 Cf. A010524, A041127. %K A041126 nonn,cofr,frac,easy %O A041126 0,1 %A A041126 _N. J. A. Sloane_ %E A041126 More terms from _Colin Barker_, Nov 05 2013