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 A078807 #11 Sep 22 2017 07:37:36 %S A078807 1,0,1,1,1,0,0,1,1,1,1,2,1,1,0,0,1,2,2,2,1,1,3,3,3,2,1,0,0,1,3,4,5,4, %T A078807 3,1,1,4,6,7,7,5,3,1,0,0,1,4,7,10,11,10,7,4,1,1,5,10,14,17,16,13,8,4, %U A078807 1,0,0,1,5,11,18,24,26,24,18,11,5,1,1,6,15,25,35,40,39,32,22,12,5,1,0,0 %N A078807 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 0. %C A078807 Row sums: 1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045). %D A078807 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 A078807 T(n, k)=T(n-1, n-k-1)+T(n-3, n-k-3)+...+T(n-2m-1, n-k-2m-1), where m=[(n-1)/2] and (by definition) T(i, j)=0 if i<0 or j<0 or i=j. %e A078807 T(6,2) counts the words 010001 and 000101. Top of triangle: %e A078807 1 = T(1,0) %e A078807 0 1 = T(2,0) T(2,1) %e A078807 1 1 0 %e A078807 0 1 1 1 %e A078807 1 2 1 1 0 %Y A078807 Cf. A078808, A078821, A079487, A123245, A077419. %K A078807 nonn,tabl %O A078807 1,12 %A A078807 _Clark Kimberling_, Dec 07 2002 %E A078807 Row 0 removed to stick to the triangle format by _Andrey Zabolotskiy_, Sep 22 2017