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 A271800 #21 Apr 15 2016 14:45:27 %S A271800 0,1,2,3,4,5,4,3,2,1,2,3,4,5,6,5,4,3,2,3,4,5,6,7,6,5,4,3,4,5,6,7,8,7, %T A271800 6,5,4,5,6,7,8,9,8,7,6,5,6,7,8,9,10,9,8,7,6,7,8,9,10,11,10,9,8,7,8,9, %U A271800 10,11,12,11,10,9,8,9,10,11,12,13,12,11,10 %N A271800 Five steps forward, four steps back. %H A271800 Colin Barker, <a href="/A271800/b271800.txt">Table of n, a(n) for n = 0..1000</a> %H A271800 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1). %F A271800 a(n) = a(n-1) + a(n-9) - a(n-10) for n>9. %F A271800 a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/9). %F A271800 G.f.: x*(1+x+x^2+x^3+x^4-x^5-x^6-x^7-x^8) / ((1-x)^2*(1+x+x^2)*(1+x^3+x^6)). - _Colin Barker_, Apr 15 2016 %p A271800 A271800:=n->add((-1)^floor((2*i-2)/9), i=1..n): seq(A271800(n), n=0..200); %t A271800 Table[Sum[(-1)^Floor[(2 i - 2)/9], {i, n}], {n, 0, 100}] %o A271800 (PARI) concat(0, Vec(x*(1+x+x^2+x^3+x^4-x^5-x^6-x^7-x^8)/((1-x)^2*(1+x+x^2)*(1+x^3+x^6)) + O(x^50))) \\ _Colin Barker_, Apr 15 2016 %Y A271800 Cf. A008611 (one step back, two steps forward). %Y A271800 Cf. A058207 (three steps forward, two steps back). %Y A271800 Cf. A260644 (four steps forward, three steps back). %K A271800 nonn,easy %O A271800 0,3 %A A271800 _Wesley Ivan Hurt_, Apr 15 2016