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 A153367 #25 Apr 22 2018 05:08:31 %S A153367 4,14,50,180,650,2350,8500,30750,111250,402500,1456250,5268750, %T A153367 19062500,68968750,249531250,902812500,3266406250,11817968750, %U A153367 42757812500,154699218750,559707031250,2025039062500,7326660156250,26508105468750 %N A153367 Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n-1 rows whose color is not that of the top right corner. %H A153367 Joseph Myers, <a href="http://www.polyomino.org.uk/publications/2008/bmo1-2009-q1.pdf">BMO 2008--2009 Round 1 Problem 1---Generalisation</a> %F A153367 Empirical g.f.: x*(4-6*x)/(1-5*x+5*x^2). - _Colin Barker_, Jan 04 2012 %F A153367 Conjectures from _Colin Barker_, Feb 11 2018: (Start) %F A153367 a(n) = (2^(-n)*((5-sqrt(5))^n*(-5+3*sqrt(5)) + (5+sqrt(5))^n*(5+3*sqrt(5)))) / (5*sqrt(5)) for n>0. %F A153367 a(n) = 5*a(n-1) - 5*a(n-2) for n>2. %F A153367 (End) %F A153367 Assuming Colin Barker's conjectures, a(2*n) = 2*5^(n-1)*Lucas(2*(n+1)), a(2*n+1) = 2*5^n*Fibonacci(2*n+3). - _Ehren Metcalfe_, Apr 21 2018 %Y A153367 Cf. A153362, A153363, A153364, A153365, A153366. %K A153367 nonn,easy %O A153367 1,1 %A A153367 _Joseph Myers_, Dec 24 2008