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 A085422 #8 Feb 10 2014 01:24:04 %S A085422 -1,2,4,13,40,125,392,1231,3867,12148,38164,119895,376661,1183315, %T A085422 3717493,11678848,36690183,115265609,362117590,1137625960,3573957358, %U A085422 11227918180,35273545269,110815110683,348135937628,1093701304102 %N A085422 A sequence analogous to the Lucas numbers (A000032), with ratios converging to Pi. %C A085422 The Lucas numbers have 1 = phi - 1/phi where this sequence has k and the ratios of the Lucas numbers converge to phi. %F A085422 a(0) = -1, a(1) = 2, a(n+2) = floor[k*a(n+1)+a(n)], where k = Pi - 1/Pi = 2.82328276.... %F A085422 Lim(n->inf) a(n)/a(n-1) = Pi. %e A085422 a(5) = floor[(Pi - 1/Pi)*40+13] = 125. %Y A085422 Cf. A000032. %K A085422 sign,easy %O A085422 0,2 %A A085422 _Gary W. Adamson_, Jun 29 2003 %E A085422 Edited and extended by _David Wasserman_, Feb 01 2005