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 A096569 #5 Mar 30 2012 18:57:05 %S A096569 1,0,1,2,2,5,9,14,25,46,78,136,242,419,733,1291,2251,3938,6905,12073, %T A096569 21129,37001,64741,113304,198344,347126,607532,1063387,1861149, %U A096569 3257410,5701362,9978711,17465052,30568232,53501720,93640745,163894183 %N A096569 Number of compositions of n with first part 1 and no equal adjacent parts; this is column 1 of the array in A096568. %F A096569 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 A096569 Cf. A003242, A096568, A096570, A096571, A096572. %K A096569 nonn %O A096569 1,4 %A A096569 _Clark Kimberling_, Jun 27 2004