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%I #6 Mar 30 2012 18:57:05
%S 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 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 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 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 Row sums: 0,1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045).
%D 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 T(n, k)=t(n, n, n+1-k), where t is the array given by A078807.
%e T(6,2) counts the words 101000 and 100010. Top of triangle:
%e 0 = T(0,0)
%e 0 1 = T(1,0) T(1,1)
%e 0 1 0 = T(2,0) T(2,1) T(2,2)
%e 0 0 1 1
%e 0 1 1 1 0
%e 0 0 1 1 2 1
%Y Cf. A078807, A078821.
%K nonn,tabl
%O 0,20
%A _Clark Kimberling_, Dec 07 2002
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