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 A123478 #18 Mar 17 2024 05:53:28
%S A123478 48,12240,3108960,789663648,200571457680,50944360587120,
%T A123478 12939667017670848,3286624478127808320,834789677777445642480,
%U A123478 212033291530993065381648,53855621259194461161296160,13679115766543862141903843040,3474441549080881789582414836048
%N A123478 Coefficients of series giving the best rational approximations to sqrt(7).
%C A123478 The partial sums of the series 8/3 - 1/a(1) - 1/a(2) - 1/a(3) - ... give the best rational approximations to sqrt(7), which constitute every fourth convergent of the continued fraction. The corresponding continued fractions are [2;1,1,1], [2;1,1,1,4,1,1,1], [2;1,1,1,4,1,1,1,4,1,1,1] and so forth.
%H A123478 Harvey P. Dale, <a href="/A123478/b123478.txt">Table of n, a(n) for n = 1..416</a>
%H A123478 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (255,-255,1).
%F A123478 a(n+3) = 255 a(n+2) - 255 a(n+1) + a(n).
%F A123478 a(n) = -4/21 + (2/21+1/28*7^(1/2))*(127+48*7^(1/2))^n + (2/21-1/28*7^(1/2))*(127-48*7^(1/2))^n.
%F A123478 G.f.: -48*x / ((x-1)*(x^2-254*x+1)). - _Colin Barker_, Jun 23 2014
%t A123478 LinearRecurrence[{255,-255,1},{48,12240,3108960},30] (* _Harvey P. Dale_, Nov 20 2016 *)
%o A123478 (PARI) Vec(-48*x/((x-1)*(x^2-254*x+1)) + O(x^100)) \\ _Colin Barker_, Jun 23 2014
%Y A123478 Cf. A123479, A123480, A029549, A123482.
%K A123478 nonn,easy
%O A123478 1,1
%A A123478 _Gene Ward Smith_, Sep 28 2006
%E A123478 More terms from _Colin Barker_, Jun 23 2014