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 A030518 #22 Mar 22 2022 18:24:39 %S A030518 0,2,8,52,248,1302,6448,32552,162448,813802,4067448,20345052, %T A030518 101717448,508626302,2543092448,12715657552,63578092448,317891438802, %U A030518 1589456217448,7947285970052,39736424967448,198682149251302,993410721842448,4967053731282552 %N A030518 Number of walks of length n between two vertices on an icosahedron at distance 2. %H A030518 Colin Barker, <a href="/A030518/b030518.txt">Table of n, a(n) for n = 1..1000</a> %H A030518 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,10,-20,-25). %F A030518 a(n) = 2*A030517(n-1) + 2*a(n-1) + 5*a(n-2). %F A030518 A030517(n) = 2*A030517(n-1) + 2*a(n-1) + 5*A030517(n-2). %F A030518 From _Emeric Deutsch_, Apr 03 2004: (Start) %F A030518 a(n) = 5^n/12 - (-1)^n/12 - (sqrt(5))^(n+1)/20 - (-sqrt(5))^(n+1)/20. %F A030518 a(n) = 4*a(n-1) + 10*a(n-2) - 20*a(n-3) - 25*a(n-4). (End) %F A030518 From _Colin Barker_, Oct 17 2016: (Start) %F A030518 G.f.: 2*x^2 / ((1 + x)*(1 - 5*x)*(1 - 5*x^2)). %F A030518 a(n) = (5^n - 1)/12 for n even. %F A030518 a(n) = (-6*5^((n-1)/2) + 5^n + 1)/12 for n odd. (End) %o A030518 (PARI) concat(0, Vec(2*x^2/((1+x)*(1-5*x)*(1-5*x^2)) + O(x^30))) \\ _Colin Barker_, Oct 17 2016 %Y A030518 Cf. A030517. %K A030518 nonn,walk,easy %O A030518 1,2 %A A030518 _Yasutoshi Kohmoto_