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 A078808 #6 Mar 30 2012 18:57:05 %S A078808 0,0,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1,2,1,0,1,2,2,2,1,0,0,0,1,2,3,3, %T A078808 3,1,0,1,3,4,5,4,3,1,0,0,0,1,3,5,7,7,6,4,1,0,1,4,7,10,11,10,7,4,1,0,0, %U A078808 0,1,4,8,13,16,17,14,10,5,1,0,1,5,11,18,24,26,24,18,11,5,1,0,0,0,1,5,12 %N A078808 Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's, all runlengths odd and first letter 1. %C A078808 Row sums: 0,1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045). %D A078808 Clark Kimberling, Binary words with restricted repetitions and associated compositions of integers, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 141-151. %F A078808 T(n, k)=t(n, n, n+1-k), where t is the array given by A078807. %e A078808 T(6,2) counts the words 101000 and 100010. Top of triangle: %e A078808 0 = T(0,0) %e A078808 0 1 = T(1,0) T(1,1) %e A078808 0 1 0 = T(2,0) T(2,1) T(2,2) %e A078808 0 0 1 1 %e A078808 0 1 1 1 0 %e A078808 0 0 1 1 2 1 %Y A078808 Cf. A078807, A078821. %K A078808 nonn,tabl %O A078808 0,20 %A A078808 _Clark Kimberling_, Dec 07 2002