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 A096570 #5 Mar 30 2012 18:57:05 %S A096570 0,1,1,0,2,4,5,10,18,29,53,95,161,283,500,869,1524,2673,4665,8170, %T A096570 14313,25032,43817,76710,134228,234938,411242,719720,1259677,2204816, %U A096570 3858882,6753956,11821191,20689807,36212093,63380145,110930372,194154783 %N A096570 Number of compositions of n with first part 2 and no equal adjacent parts; this is column 2 of the array in A096568. %F A096570 Define s(0)=1, T(1, 1)=1 and T(i, j)=0 for j>i. For n>=2 and 1<=k<=n, define s(n)=T(n, 1)+T(n, 2)+...+T(n, n) and T(n, k)=s(n-k)-T(n-k, k). (This is array A096568.) %Y A096570 Cf. A003242, A096568, A096569, A096571, A096572. %K A096570 nonn %O A096570 1,5 %A A096570 _Clark Kimberling_, Jun 27 2004